Actually, I did read the FAQ, but that particular item didn't mean much to me at the time. Well, now it does! That was the problem in my case, PIO mode.
I think the problem might be that the previous drive in that slot was a CD writer, and the device got set to PIO. Anyway, I uninstalled the secondary IDE channel and let Windows reinstall to get Ultra DMA mode 2 to stick. Now it works fine, and is burning my Sony 8X media at 8X. I also have some Verbatim 16X DVD-Rs I will try to see if they actually burn at 16X as well.
By the way, both the drives (the old Toshiba 4X burner and the new Plextor) are set to Cable Select. This does not seem to be a problem, since they are both now keeping the Ultra DMA mode 2 setting. I mention that since one of the responses said Plextor likes to be set at Master.
In any case, thanks for the help! (Y)