Car Update:
Went to my local oil change/tune-up place today, and they discovered that the antifreeze needed to be flushed, as it wasn't getting to the engine. That, and an oil change and a much-needed swap out of the windshield wiper blades, took care of the problems I've been having, and at just over $100, that's not too bad for routine maintenance. Nice when things aren't as expensive or catastrophic as you expect.