Navigator....I think it is more probable that it was completed in the midst of the events, since the end of Antiochus IV in 164 BC is not as how it is described in 11:40-45, tho there is much uncertainty as to whether the book circulated before or after the rededication of the Temple in 165 BC (i.e. are the specified time periods an attempt at forecasting the restoration of the Temple by the author, or a reporting of the actual events?). The narrative portions in ch. 1-6 (with the possible exception of ch. 2), meanwhile are generally thought to precede the Antiochene crisis and may have circulated independently c. 200 BC or earlier (cf. the highly variant text tradition in ch. 3-5 in the Greek).
a Christian....That's quite an interesting and novel interpretation. My biggest reservation about it is the fact that it designates the erection of the heathen altar as the time the Temple was "cleansed," which as you note is a difficult idea to swallow....that this would have seemingly been the time "the temple was more defiled than before". I do not believe the author of Daniel conceived of Antiochus' assault on the Temple in 168 BC as a positive cleansing away of the practices of a corrupt high priest (whom you identify as the "abomination which causes desolation"), for the description of this assault in ch. 11 is designated as the installation of the "abomination" and not its end. Thus the accession of Antiochus IV Epiphanes in 175 BC is mentioned in 11:21, followed by the "crushing of the ruler of the covenant" in v. 22....which would naturally correspond to the assassination of the legitimate high priest Onias III in 171 BC (cf. the "cutting off" of the anointed one in 9:26, and the "dashing to pieces" of the lamb in 1 Enoch 90:8). It is at this point that Menelaus is made high priest (2 Maccabees 4:23-35). This is confirmed by the reference a few verses later (v. 25-27) to Antiochus' invasion of Egypt in 170 BC, the first part of which ended with a victory near Pelusium (v. 25; cf. 1 Maccabees 1:16-19, "the first expedition against Egypt" implied in 2 Maccabees 5:1), and then Antiochus "will return greatly enriched to his own country," having had his "heart set against the holy covenant he will take action and then return to his own country" (v. 28). This may be reference to Antiochus' plundering of the Temple on his return to Syria from Egypt in 170 BC (cf. 1 Maccabees 1:21-28), whereas 2 Maccabees 5:11-20 dates the plundering to 169 BC, following Antiochus' "second expedition against Egypt" (2 Maccabees 5:1). This second war against Egypt is clearly mentioned in Daniel 11:29, "in due time he will make his way southwards again but this time the outcome will not be as before" because of opposition by the "ships of Kittim" (v. 30), and indeed Polybius described Antiochus' encounter with the Romans during his unsuccessful expedition against Ptolemy VI Philometor, during which Antiochus "replied that he would do whatever the Romans demanded" and he "withdrew his army into Syria ... groaning in spirit" (29.27). Similarly, Josephus (Wars of the Jews, 1.1.4) describes how Judas Maccabeus made an alliance with the Romans who "drove Epiphanes out of the country when he had made a second expedition into it, giving him a great defeat there". According to Daniel 11:30, it is when Antiochus retires to Syria that he "takes furious action against the holy covenant", perhaps this is the allusion to the plundering of the Temple that 2 Maccabees places after the second expedition. Thus, by this point in the text, we already have two expeditions against Egypt, "furious action" taken against the holy covenant, and the crushing of the high priest before all of this. All of this happens by 169 BC. It is after then, and only after then, that the text next states that the abomination of desolation (= "appalling horror" in the Hebrew) is set up:
"Forces of his will come and profane the sanctuary citadel; they will abolish the perpetual sacrifice and install the disastrous abomination there" (Daniel 11:31).
The reference to "forces" of Antiochus invading the Temple and abolishing perpetual sacrifice and installing the abomination is clearly to the traumatic events of 168 BC described in 1 Maccabees 1:29-61 ("two years" after Antiochus' first expedition against Egypt in 170 BC, 1:29), which describes the "impressive force" of Antiochus' mysarch pillaging Jerusalem (v. 30-31), "defiling the sanctuary itself" and shedding innocent blood around it (v. 37), and sometime after this the king directed the Jews to "profane the sabbath ... banning holocausts, sacrifices and libations from the sanctuary, profaning sabbaths and feasts, defiling the sanctuary and sacred ministers" (v. 43-46), culminating on the erection on the 15th of Chislev of "the abomination of desolation above the altar" (v. 54), clearly identifying the abomination of Daniel with the heathen altar that Antiochus had erected. The events of 168 BC were not viewed as cleansing the Temple but the exact opposite. The text describes all the elements of Daniel 11:31 in the same order: (1) the arrival of an impressive military force, (2) the defiling of the sanctuary, (3) the abolition of holocausts, sacrifices and daily libations at the sanctuary, and finally (4) the erection of the "abomination of desolation". The context of Daniel 11:31 also places this event at the same time as 1 Maccabees: AFTER the Egyptian expeditions, not BEFORE them as your interpretation requires (i.e. the installation of Menelaus as the high priest in 171 BC), and historically Menelaus was not made high priest through military force. Since we know that Antiochus did completely ban all sacrifice and offering in 168 BC, and this was to last for 3+ years, this better fits Daniel's references to Antiochus "abolishing the perpetual sacrifice" (8:11), to the "coming ruler" who "puts a stop to sacrifice and oblation and the disastrous abomination will be in their place" (9:27), and to the forces of Antiochus who "will abolish the perpetual sacrifice and install the disastrous abomination" (11:21). True, Menelaus and Jason were careless with observing the sacrifice and introduced heathen customs (2 Maccabees 4:12-14), but they did not completely abolish the sacrifice as 1 Maccabees says Antiochus did and as Daniel claims that Antiochus himself would do. What I don't understand is how you describe Menelaus and Antiochus as "cleansing the temple of corrupt Jewish religious practices" by instituting complete heathenism, when the corruption of Jason and Menelaus that preceded this was precisely the introduction of "hellenizing practices" into the Temple, contrary to the Law (2 Maccabees 4:11-14). It was not the defeat of hellenization that occurred in 168 BC but its total victory over Law-observant Judaism, to the extent that those who remained faithful to the covenant (i.e. who had not given in to hellenizing practices) were persecuted and put to death, as 1 Maccabees 1:57-61 describes in gory detail. It is just this persecution that is described in Daniel 11:32-35, again fitting perfectly into the 168-165 BC timeframe. The removal of the abomination, moreover, is described in 1 Maccabees 4:43, 6:7 as occurring in 165 BC during the purification of the Temple: "Next he selected priests who were blameless in observance of the Law to purify the sanctuary and remove the stones of the Abomination to an unclean place" (4:42-43). The priests cleansed and purified the sanctuary, along the lines of the Law in Exodus and Leviticus, which included anointing the place with chrism, just as Daniel 9:24 refers to the "anointing of the Holy of Holies" as part of Jerusalem's final restoration. This occasion, the rededication of the Temple by the priests as celebrated to this day in Channukah (cf. John 10:22-24), imho best fits the historic event expected by the author of Daniel (during which "the sanctuary will have its rights restored", 8:14).
As for whether ch. 9 refers to a completely different "abomination of desolation" and defiling of the sanctuary than described in ch. 11, I see the only reason to disregard the obvious parallelism between the two oracles is the NT mention of the "abomination of desolation" as still future, which for some rules out entirely the possibility that ch. 9 refers to Antiochus Epiphanes. This is not based on exegesis of the text itself but on a stipulation that a particular later interpretation of this text must be correct (on the basis of a belief in biblical inerrency). However, I do not believe this is an either-or proposition. True, the apocalyptic interpretation given in the synoptic gospels is a later interpretation of Daniel, for the Antiochene interpretation is attested much earlier. But it would still be possible to maintain both interpretations by assuming a type-antitype relation between them as various Christian interpreters have done over the years, viewing Antiochus as a type of the Antichrist or as a type of Titus. This is how Josephus apparently understood the passage. He understood that Antiochus Epiphanes was the focus of the oracle in ch. 8 (as the one who despoiled the Temple and forbid sacrifices "for three years", i.e. the time period between Chislev 168- Chislev 165 BC) and yet the same prophecy also looked ahead to the Romans despoiling the Temple (Antiquities, 10.11.17). Similarly, he elsewhere referred to the period during the Antiochene crisis as the fulfillment of Daniel's prophecy of the Temple being desecrated:
"So on the five and twentieth day of the month Chislev, which the Macedonians call Apelleus, they lighted the lamps that were on the candlestick, and offered incense upon the altar ... these things were done on the very same day on which their divine worship had fallen off, and was reduced to a profane and common use, after three years' time; for so it was, that the Temple was made desolate by Antiochus, and so continued for three years. This desolation happened to the temple in the hundred forty and fifth year [i.e. 168 BC], on the twenty-fifth day of the month of Apelleus, and on the hundred and fifty-third olympiad, but it was dedicated anew, on the same day, the twenty-fifth of the month Apelleus, in the hundred and forty-eighth year [i.e. 165 BC], and on the hundred and fifty-fourth olympiad. And this desolation came to pass according to the prophecy of Daniel, which was given four hundred and eight years before, for he decalred that the Macedonians would dissolve that worship for some time" (Antiquities, 12.7.6).
Note that in Wars of the Jews, praef. 7, and 1.1.1, Josephus states that "Antiochus Epiphanes took Jerusalem by force and held it for three years and three months", and that "he also spoiled the Temple and put a stop to the constant practice of offering a daily sacrifice of expiation for three years and six months," here reflecting the time periods of Daniel. So too Josephus is thought to allude Daniel 9:25 in Wars of the Jews 6.5.4, and 9:26 in Wars of the Jews 4.5.2, in applying the prophecy to contemporary events, the latter reckoning the beginning of the fall of Jerusalem from the assassination of high priest Ananus seven years before AD 70 (cf. the "cutting-off" of the anointed one at the start of the 70th week). One thing to keep in mind is that the Christian messianic interpretation of ch. 9 of Daniel is distinct from the Roman interpretation attested in the NT, Josephus, and Jewish and early Christian exegetes. Some Christians applied the prophecy entirely to the destruction of Jerusalem (cf. Pseudo-Clementine Rec. 1.64), others applied it to a still-future Antichrist (Irenaeus, Adversus Haereses 5.25.4), neither of which relating the prophecy to Jesus Christ. The author of Revelation moreover takes up the time periods and actions of Antiochus in Daniel and applies them to a still-future Antichrist (= the Beast). The Christian messianic exegesis appears only in the third century AD onward, and on the authority of the NT it merges the messianic interpretation with the earlier Roman/apocalyptic interpretation. The mainstream modern Christian interpretation likewise mingles the originally distinct interpretations. Thus the messianic view itself does not appear in the NT, while the Roman/apocalyptic interpretation in the gospels could be recognized as a subsequent re-interpretation of Daniel and/or an antitypical fulfillment in the future of the type of Antiochus and his defiling of the Temple (either by Titus or by a future Antichrist).
