Earnest,
I meant "imply" in exactly the same constraining sense as you use "have to imply" (the latter sounds pleonastic to me, but then maybe I am influenced by the French impliquer which strictly... has to imply a necessary implication ;)). Of course the double article and/or possessive can apply to two referents (as in "my dog and my cat") or just one ("my Lord and my Master").
In 20:28 I don't think a difference in referents is seriously arguable from the context but the titles kurios and theos are kept separate unlike v. 17. It's not one title (as in Titus 2:13 or Jude 1:4 for instance). There is a shift from the common Christological title (kurios) to that which is (so far) specific (if not exclusive) to the Johannine faith (theos). If I can risk an interpretation, Thomas finally "sees" what is really to be seen in Jesus; the revealed One in the Revealer. Cf. 14:8f and the thematic of seeing and believing throughout the Gospel, which also occurs in v. 4-8 (both Peter and the Beloved disciple see, only the latter believes -- hence really sees).
I took Revelation 4:11 as the first example that came to my mind and didn't care about the variant readings, let alone the NWT rendering. But it's good you bring it up because I now see that the NWT here ruins the construction, where the possessive applies to both terms (which could not happen with a personal name in either Biblical Hebrew or Greek: you don't say "our Yhwh" or "my Jesus" of "your Moses"). So as you noticed the first article is simply suppressed along with kurios) and the embarrassing kai which follows becomes an awkward intensive "even"... that would be worse (if possible) in the Sinaiticus reading as the remaining possessive would be incomplete without the article (unless you take it in the sense of "Jehovah, even a god of ours").
Btw according to the NA27 critical apparatus (I have lost your link to the ms facsimile, but you might check it up) the Sinaiticus actually reads kurie ho kurios kai theos hèmôn, where the first kurie (vocative) is a clearer functional substitute of the DN (not "implying" that the DN itself had to be there in some edition of Revelation in any other form than a substitute of course).