Thanks to all who responded. Here's what I've learned.
1) Switching from APM to ACPI (in the kernel configuration) broke the Fn+F7 
key sequence to the point I couldn't switch the video jack on/off. (It was 
apparently on all the time with ACPI.) I re-gen'd the kernel with APM and was 
able to cycle through the LCD-Only / Video-Only / LCD&Video Both settings 
that previously solved the swimming, and that still works. So, I had a 
fall-back work-around.
2) The system have both an XF86Config and an XF86Config-4 file and, with the 
help of a posting here (from "Voltage Spike"), I hid the XF86Config and 
restarted X to verify it was actually using XF86Config-4, and it was. (I 
think I rebooted, actually.)
3) I tried Xconfigurator, pretty much let it do the guesswork and it 
generated an XF86Config file. Temporarily moving aside XF86Config-4 and 
restarted X. Not seeing any apparent change, I rebooted but, again, no change 
in the swimming.
4) Looking in /usr/share/doc/XFree*4*doc, I found a reference to xf86cfg for 
generating the XFree86 version 4 configuration file. I gave it a shot, 
changed the vertical refresh to 60.03 (as close as I could get to 60) and 
tried that. Zowie -- what a flicker!!! Bad, bad, bad.
     At this point I decided I had blown enough time and decided to go back 
to the XF86Config-4 file that came with RedHat. I suppose the next step 
would've been to go back to xf86cfg and try some other settings and find a 
good combination. I did notice, however, that the appearance I would see 
using the xf86cfg "Apply" button was VERY different from what I would see 
after having xf86cfg write a configuration file and then restart X. My 
impression is that xf86cfg is broken, but Xconfiguration is for the old XFree 
(version 3).
     Anyway, thanks for the suggestions and the opportunity to learn a little 
more about XFree. (At least I know *which* configuration file is *really* 
being used on my system now!)

-- 
Ed Skinner, ed@flat5.net, http://www.flat5.net/