I'm happy to report that my cable modem was replaced this morning. Running a speed test on the old one produced numbers like this:
The new one is considerably better and actually provides the bandwidth I'm paying for. Which is nice.
It took the service tech an hour or so of other troubleshooting before he replaced the modem. Everything I've heard indicates these cable modems being flaky and often need to be replaced. Cable companies could probably cut a fair chunk of time out of their service call time by switching out the cable modems earlier in the process. Especially when the customer (me in this case) is a techie and has already checked everything else.