Actually, after fiddling with it for a while, it seems that I was overdriving the video card with the nv driver and never realized it.
The nvidia driver reports that the card has a maximum clock of 215MHz or so. In configuring my display, I hadn't used a range, but rather had used the specific frequencies listed in a table that came with the monitor to get 1600x1200 at 85Hz, 106.3h & 85v. The table also specifies that this requires a clock of 229.5MHz. So that's why it wasn't working under the nvidia driver. Oops.
I fell back to specifying a range (30-121h & 48-160v) and the nvidia driver came up just fine at 1600x1200, albeit only at 75Hz. And my Xvideo drivers were now working. Unfortunately, video playback was mangled by some really nasty artifacts. Which is fine, I guess, since I wasn't wild about running at 75Hz anyway.
Oh well. I'll be replacing this 21" tube with a 19" LCD that runs 1280x1024 soon enough anyway. I'll try it all again then.