Radeon 7000/VE
I never thought I'd be happy to see 114 frames per second out of
glxgears, but that's double what I was getting before, so I claim
success. I suspect if I cranked the resolution down from 1600x1200 to
something a little smaller, or dropped the color depth down to 16bpp, I'd
get a little better performance, but frankly, I'm not really willing to
sacrifice either. Call me spoiled. 
For the curious: lspci identifies my card as a Radeon RV100 QY
(Radeon 7000/VE), which is apparently some bastard child of the Radeon
7000 lineup that has a bad time with DRI. It also has the fact that it's
a PCI card working against it, but hey, at least it's got 128MB of
painfully-slow-to-access video memory onboard. 
Two initial problems cropped up: first, I had an MTRR conflict which
required manual intervention to clear up (I found a thread over at
Rage3D.com
that put me onto a solution for that), and second,
DRI is disabled on the
Fedora build of
Xorg, and needs to be explicitly re-enabled
for the Radeon 7000/VE (add Options "DRI" to the Device
section of xorg.conf). Basic desktop behavior is a bit quicker now, and
video playback is actually doable now, so it's a good place to stop for
the night, but this is truly terrible performance compared to what I was
expecting.