I went in to the hand surgeon today to go see what he thought about my broken finger. In hand was the X-ray I had yesterday, in which I was not able to discern any improvement. He took one look at it, though, and said, "Oh, yeah, it's filling in." Apparently the bone is indeed repairing itself and I'm just being paranoid.
I also had the chance to visit with a few friends yesterday who have had broken fingers in the past. They let me know that the healing of a finger takes months, a sentiment which the doctor echoed to me today, which was reassuring.
The doctor changed my instructions, though. He said I no longer need to buddy-tape the finger, nor do I need to keep it wrapped all the time -- only when I'm doing "work". It was unclear to me whether or not that meant typing, so I'm going to assume it does not. But hauling things around, lifting kids, and other activities where the finger can be jarred are no-nos. He did say that the thing to avoid the most is twisting the finger; if I should do so, that would make him "happy".
In any case, it looks like I will have it wrapped for a long time, but he does want me to work on bending it to try to improve my mobility. My goal is to be at 100% by April, which seems achievable.