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.