Well, I solved my problem, and I'm writing this to help anyone else who might encounter a similar situation.
The first thing I need to make clear is that in the original post I noted that the drive had problems reading cd-rws that were just written. I've since confirmed that the problem was in the writing, not the reading, as the cd-rws written in this drive couldn't be read in other drives either.
Anyway, after further troubleshooting on my own, I called Plextor tech support. The support person was very nice and spent quite a bit of time with me over the phone. What he told me was that the drive has two lasers: one for all cd operations and one for all dvd operations. Since the drive tested fine with the internal self-test and could read/write cd-rs with no problem, then the problem wasn't the drive. He suggested a couple of options, including disabling the IMAPI cd writing service and upgrading InCD.
Neither of these options proved fruitful, so I decided to try swapping the drive (with the same model). Since then, everything has worked perfectly. The original drive apparently had a problem writing to cd-rw media, but was fine with cd-rs. Plextor tech support turned out to be dead wrong. I know that packet-writing sofware can be buggy so everyone's first inclination is to blame the sofware, but for once InCD wasn't to blame here.
Anyway, the problem is solved. Thanks to everyone for their suggestions and time.