Problem is, the log isn't able to tell us which application is causing that.

Do you think you could try to SSH into the machine while the screen hard
freezes and check with top/htop if there is anything consuming lots of CPU? And
see if killing that application unfreezes the screen?

If the only application consuming significantly more CPU is Xorg, maybe killing
applications inside the Xorg session until it unfreezes could help us track
down which application is causing that freeze.