I'm feeling pretty confident that ScoreCenter was the problem. The network traffic that the widget was generating was causing quite a battery drain, I think. It turns out that some of the more recent post-Froyo reviews of ScoreCenter in the Marketplace mentioned heavy battery drain as well as overall updating problems with the ScoreCenter widget since Froyo came along. I can still use ScoreCenter without using the widget and avoid the power hit, so that's good news. I hope the developer of that app gets wise to the issue and fixes it, because that was one of my favorite widgets. If not, I could always try another sports score app, but I alread went through that process and liked ScoreCenter the best.
Oh well, at least I can actually stop worrying about killing my phone battery during throughout the day now, and start using it normally. I will also be re-implementing the Facebook widget since I'm pretty sure now that it was never the problem in the first place. Now I'll see for sure.
-SR-
The "testing" screen brought up by putting *#*#46364#*#* was of paramount usefulness in diagnosing this issue. I wish I had known about it sooner. Great feature!