Comment # 25 on bug 1188954 from Stefan Dirsch

You could check which DRM drivers have been added to initrd by running

  lsinitrd /boot/initrd | grep drm

I believe only the needed (default) driver is being added to initrd. So, yes it
would make sense to force dracut to add "amdgpu" driver and save space and not
include "radeon" driver. As you suggested

force_drivers+=" amdgpu"
omit_drivers+="radeon"

Of course you need to regenerate the initrd afterwards.

Xserver is being started by the displaymanager. So if anyone can/should wait
for existence of /dev/dri it would be the DM. But I'm afraid this won't help.
As you noticed the load of the module is being triggered by Xserver, the device
is just not available in time.