Today I finally made decent progress on this issue. I can confirm that the GPU
lockups are not the X server's fault, since they appear also when using weston
and indeed, when running the eglkms Mesa demo on the pure framebuffer.

Trying to find the exact OpenGL call that causes the lockup, I discovered, that
when I change the power profile before starting any GL program (Mesa demo or
display server), it continues to work until the next reboot. So all that was
needed was a
echo low > /sys/class/drm/card0/device/power_profile
executed before starting the X server and I could change power profile at
runtime.

I then turned on dpm again and indeed:
echo high > /sys/class/drm/card0/device/power_dpm_force_performance_level
echo auto > /sys/class/drm/card0/device/power_dpm_force_performance_level
called by an ExecStartPre script from the display-server service file fixes the
issue completely for me and I have now a fully working dpm :)

So it seems like the first change of performance level/profile initializes
something that must be initialized before the first GL call or CRTC change for
power management to be stable. Any idea what this something might be?