Excellent job, Doug. I think you lay out the complexities and problems very well. You show that the interpretation the Society claims is self-evident is actually not supported by the text itself. The purpose and intent of ch. 9 rather comes into focus when it is understood that it is talking about the same thing that the visions in ch. 8 and 10-11 are concerned with: the sanctity of the Temple in the post-exilic period, climaxing in the defiling of the Temple under Antiochus Epiphanes (the "little horn" from the kingdom of Greece in ch. 8). The question of "how long" from ch. 8 receives a specific answer in the periodization scheme of ch. 9, and the question of "why" the Temple remains in such a state so long after the return from Exile is also answered by the angel. The scheme the author adopts is intelligible because it is interpretive of both Jeremiah and Leviticus (it uses Leviticus to interpret Jeremiah), such that the 70 years is expanded into a duration of 490 years on account of the "sevenfold" curse (the curse alluded to in Daniel 9:11). This is a time period determined not by actual chronological concerns but ideological ones.
As you point out, the chapter is not concerned with the timing of the arrival of the Messiah. There is nothing about this in the prayer that Daniel gives; he is asking for the curses against Jerusalem and its Temple to come to an end. It is the same with ch. 8, which inquires on when the defiling of the sanctuary would come to an end so that it would be reconsecrated (v. 13-14). The Society's interpretation in fact has the seventy weeks end with the Temple, if not yet ruins (soon to be in AD 70), being rendered wholly illegitimate to God, whereas v. 24 makes clear that the period is one in which the holy city atones for its transgression, ending with its being brought to a state of everlasting righteousness (again, compare with 8:14). The messianic interpretation is forced from the text by the NWT rendering of Hebrew mshych as "Messiah" (the only place in the OT where the NWT renders the word this way in the text), and from the conflation of the two "anointed" figures in the text into a single Messiah. The term usually has the meaning "anointed one" applied to kings and priests in the OT and within the context of the discussion in ch. 8-9 of the Temple, a sacerdotal sense is manifest here (especially with respect to the anointing of the Holy of Holies in v. 24). The conflation of the two anointed figures, encouraged by Theodotion's version (which replaced the LXX in early Christianity), is not permitted by the MT's punctuation, which has a period of some 62 weeks separating the two anointed figures apart. This is supported by the immediate context and syntax, as well as by the early interpretations of the text found in Hippolytus and others (in spite of the fact that their translation was that of Theodotion). The duration is that of the post-exilic high priesthood, marked off by its institution after the exile (the coming of the anointed one in v. 25) and its end at the start of the final week (= the deposing and assassination of the high priest, cf. 11:22). The Testament of Levi, for instance, viewed the seventy weeks as a time of corruption for the post-exilic priesthood. What is especially conspicuous is that the Society's interpretation relates the cessation of sacrifice and offering, which was effected by Jesus' willing submitting to crucifixion in AD 33 (offering ceased in the sense that it was no longer acceptable to God). But within the context of the Hebrew apocalypse, the cessation of sacrifice and offering was effected by the "little horn", the Gentile king who was an antagonist against God and his Temple (see 8:11-13, 11:31). Indeed the reference to the"armed forces who descecrate the sanctuary fortress and abolish the daily sacrifice and set up the abomination of desolation" in 11:31 is clearly parallel to the references in 9:26-27 to the "people of the ruler who will come will destroy the city and the sanctuary", with the ruler "putting an end to sacrifice and offering" and "setting up" the abomination(s). Within the context of Daniel, the one who puts an end to offering is a villianous figure, not messianic. And it is not clear to me who the "ruler who is to come" is supposed to be in the Watchtower interpretation. But reading ch. 9 in connection with ch. 8 and 10-11, this figure is clearly cognate to the "little horn" of ch. 8 and the villianous king of ch. 11. The Watchtower interpretation also vaguely connects the final desolation of Jerusalem (and the setting up of the abomination of desolation) in 9:27 with the destruction of Jerusalem in AD 70. This draws on the interpretation of ch. 9 and 11 found in the synoptic gospels, which related the terminus of the seventy weeks to Jewish Revolt and war. But there is no explanation of how to stretch this week all the way to AD 70 (which already is interpreted as terminating with the conversion of Cornelius) without assuming some sort of gap (a gap is also common in modern dispensationalist interpretations), though there is no indication whatsoever of a gap in the text.
