Thank you for your reply, Nutlaw, and some further research may have uncovered my problem. Apparently it's related to the "faces.dat" file: after one of my crashes I noticed that file's size changed from about 3.5 MB to 0 MB. That lead me to search for "faces.dat" on the forums and I came up with
several previous threads detailing just the kind of problem I'm having. I just this moment have finished testing battists's suggested fix of renaming "faces.dat" to "faces.old": sure enough, I've been able to sim into 2011 (and counting) without a crash. The downside is that all player pictures will have to be regenerated, which is definitely a shame but certainly not the crisis that the crashes were.
I haven't yet fully regenerated all player pictures. Until I do that I'll hold off on saying I'm 100% fixed, but it certainly looks like this will do the trick. I'll report back when I've finished recreating my pictures and have tried simming again.
Also, to answer your questions: Both computers are using Win XP SP2. Computer #1: Recently defragmented, short on HD space. Computer #2: Not recently defragmented, lots of HD space. 11 leagues w/ 208 teams in our universe. No unusual end-of-year settings that I can think of (including retirement/HoF). Draft pick compensation is on. FaceGen is being shut off from the program entirely (in the OOTP preferences screen), but was originally on when the league was created. The start point for this test had our league advanced two days in game and pictures for all players in the universe generated.