The solution to my iMessage problem
It turned out that the solution to my iMessage problem was relatively straightforward. That said, it only worked because I still had my old phone (it hadn’t been stolen; I hadn’t traded it in; etc.). It also worked when doing things like going to Apple’s site and deauthorizing my devices didn’t (which I still don’t understand). So the problem I pointed out really is a serious bug.
But for me, I had the phone and the solution (as a few people suggested in the comments to my post) was as simple as disabling iMessage on my device. Apparently this triggered a reset on the Apple server such that messages sent to me were no longer being routed through iMessage, thus fixing my problem. Problem solved.
Now if I could only stop incoming texts from coming in double (apparently a bug with the latest Handcent SMS build)…