I finally got things working on this machine, and I figured I'd follow through and post my findings just in case it's helpful to someone else.
To recap, I'm running on an Alienware Area 51m, with the 15.4" WSXGA+ screen and an nVidia FX5600 Go card. I was using RedHat 9 with a self-compiled 2.4.22 kernel. I tried upgrading to Fedora Core, but had many problems, and am now running Mandrake 9.2.
I got things working using the nv driver by following martin.christen's directions here:
I also had to get different modelines, which I was able to generate using the following site:
So I had it working in full 1680x1050 glory, but I had no hardware acceleration (OpenGL apps just wouldn't run) and piss poor framerate in everything else.
Finally, after much experimentation, I was able to get it to work using nVidia's 1.0-4496 drivers by setting the following option in my XF86Config-4:
Option "NvAgp" "0"
Without the above setting, or by using a value of 3 or 4 would cause my machine to lock into a solid black screen when starting X. (Must be something to do with agpgart, but I don't know what.) Setting it to 1 (using nVidia's agp driver) would work, but only if I booted to Windows first and then did a soft reboot into Linux. But setting it to 0 (no agp) makes it run just fine from a cold boot. At last!
Now, I'm not sure what other ramifications disabling agp might have, but at least the thing works.