No, I can't access another tty during a freeze, unfortunately.

That's may be a hint!

The only times I've had the desktop freeze on Linux and the alternate terminals fail to respond, I had a hardware issue.

In one case, I was on a Raspberry Pi, and my power supply was not delivering clean enough power for the board.

In another case, my fan wasn't connected properly and the motherboard was overheating.

Edit: Oh! I think I had this behavior once with a RAM stick that was terribly subtly not quite all the way in the slot.