I should point out that Melchizedek does not really mean "My king is Jupiter", it means "My king is Zedeq". In later rabbinical times, tsedeq also was used to refer to Jupiter. I'm not sure how early this usage was, it's not known if this was also the case when the OT was written, it could have been. But the point I made in the other thread is that there is no evidence that the Canaanite god Zedeq, whose name is probably contained in the name Melchizedek, was identified with Jupiter. Now Zedeq was associated with Shamash the sun god as a hypostasis, whereas Jupiter was always associated with Marduk, the tuletary deity. Now it is possible, even probable, that there could still have been a connection. So for instance, at Baalbeq in Syria there was a temple to Jupiter Heliopolitanus which drew on the Shamash cult, though it is not clear if this cult had anything to do with the planet Jupiter. Also Mark Smith mentions how Marduk was syncretized or Shamash or otherwise solarized:
In Assyria, the solar disk, originally the symbol of the sun-god, Shamash, was used for the national god, Assur. 610 Similarly, “Babylonian theologians” (to use W. G. Lambert’s term) call their national god, Marduk, the “sun-god of the gods” in Enuma Elish 1:102 and 6:127. 611 A small god-list identifies various deities with specific functions of Marduk. 612 Shamash is the “Marduk of justice.” Another text states that “Shamash is Marduk of the law-suit.” 613
But this was a probably a later development of the first millennium BC, earlier Shamash was a clearly distinct deity. And there is no evidence that Zedeq was associated with the Jupiter per se, much less in the Bronze Age when Melchizedek supposedly lived.
As for the story of Jupiter aiding Abraham, this is appears in Ginsberg from a late midrash:
The battle fought with the mighty hosts of the kings, from which Abraham emerged victorious, happened on the fifteenth of Nisan, the night appointed for miraculous deeds. The arrows and stones hurled at him effected naught, but the dust of the ground, the chaff, and the stubble which he threw at the enemy were transformed into death-dealing javelins and swords. Abraham, as tall as seventy men set on end, and requiring as much food and drink as seventy men, marched forward with giant strides, each of his steps measuring four miles, until he overtook the kings, and annihilated their troops. Further he could not go, for he had reached Dan, where Jeroboam would once raise the golden calves, and on this ominous spot Abraham's strength diminished.
His victory was possible only because the celestial powers espoused his side. The planet Jupiter made the night bright for him, and an angel, Lailah by name, fought for him. In a true sense, it was a victory of God. All the nations acknowledged his more than human achievement, and they fashioned a throne for Abraham, and erected it on the field of battle. When they attempted to seat him upon it, amid exclamations of "Thou art our king! Thou art our prince! Thou art our god!" Abraham warded them off, and said, "The universe has its King, and it has its God!" He declined all honors, and returned his property unto each man. Only the little children he kept by himself. He reared them in the knowledge of God, and later they atoned for the disgrace of their parents.
Traditions in such late sources usually reflect biblical exegesis and haggadaic storytelling than genuinely early traditional material. This detail in particular is not found in early retellings of the story in the Jubilees, Genesis Apocryphon, Josephus, or Pseudo-Philo. The tradition seems to come from Genesis Rabbah 42.3. This makes an interesting parallel for how the stories of Jesus in the NT draw on OT traditions of Moses, or David, or other personages. The midrashic retelling of Abraham's battle against the kings draws on the story of the Exodus.... the battle occurred on the evening of Nisan 15 when the Exodus occurred (Pirqe d'Rabbi Eliezer 17), there was an angel called Night (Lailah) that attacked the enemy (Sanhedrin 96a), like the Destroyer that killed the Egyptians the night of the Exodus, and so the tradition that Jupiter made the night bright for Abraham and his men is reminiscent of the pillar of fire that lit the way of the Israelites during the Exodus, but yes there might also be a borrowing of the motif from Joshua of the sun and moon standing still. But knowing usual midrashic procedure, the text itself occasioned these details...."During the night" in Genesis 14:15 was interpreted as "the night(Lailah) was divided against them", i.e. the Night was itself on Abraham's side against the kings, and this was combined with Isaiah 41:2 ( Who has stirred up one from the east, calling him in righteousness(tsedeq) to his service? He hands nations over to him and subdues kings before him. He turns them to dust with his sword, to windblown chaff with his bow"), which also produced the references to chaff and dust.