I finally am trying to set the GART size, as per Alex's comment #12.

Without setting it, Xorg0.log reports:
[    15.054] (II) RADEON(0): mem size init: gart size :1fdef000 vram size:
s:20000000 visible:1f020000

The default GART size is 512MiB, You'd think that would be a good match for the
512MiB video RAM on my card.  This output shows that the GART size is reduced
by a somewhat odd number (13^2 * 2^12).

When I set radeon.gartsize=1024 on the kernel line, Xorg.0.log reports:
 [    14.842] (II) RADEON(0): mem size init: gart size :3fdef000 vram size:
s:20000000 visible:1f020000

Again, the GART size is reduced by the same amount.

Wait: according to http://dri.freedesktop.org/wiki/GART/ the GART seems to
enable the video card to access the computer's memory, not the other way
around.  So I don't see how this is relevant: we're getting a crash in a CPU
instruction that is trying to access the video card's memory.