I know, I should just reinstall. But I've been too busy to risk that much disruption when I don't currently have a good backup solution, and I seem to have figured out how to avoid the crashes most of the time.

I noticed fairly quickly that the crashes seem to always be related to modem use: they happen either while the modem is disconnecting, or very quickly thereafter. And I also noticed, shortly before the crashes started happening, that disconnecting was taking a lot longer than it used to. Something's up.

After playing around for a while, I figured this out: if I unplug the phone cord from my laptop before I tell the modem to disconnect, the machine won't crash. So far, that's worked. Keeping my fingers crossed.