Just as a coda to this whole mess...
Most people, when they have a problem they rarely tell you of the resolution, but I figured I'd shine some light on it since I'd been especially bitchy about it.
Officially I'd been labeling this as a problem since the day my Xbox RRoD'd on me.
That would make as of today, exactly 14 weeks (98 days) to get my Xbox Licensing fixed, seeing as how the Xbox red ringed on December 18th.
Technically, the case has been open for me to get my license transferred on all my games since January 30, or 74 days.
Take it however you will, but I just got a phone call about 15 minutes ago from "Mark" at Xbox Live Support telling me that my licenses for all my games have now been transferred from my older and broken Xbox 360 to the new one. Huzzah.
I won't actually be able to test this until I get home tonight, but the prospect of playing Ms. Pac Man without being online is somewhat comforting, I suppose. I did pay for it after all.