Ok, I installed -dbg packages for mesa/radeon, didn't and had no luck using gdb
(or I don't know how to use it to debug radeon/mesa drivers), but I had luck
getting some debug out of R600_DEBUG.

Please note "radeon: The kernel rejected CS, see dmesg for more information."
and "radeon: Failed to deallocate virtual address for buffer:" in the
R600_DEBUG.txt file.

I had 400MB of syslog filled with errors, I took just last 500 lines to upload
here.

Hope this will help a bit more with solving the issue.
Please advise what can I do more.