I was having problems with the same server locking up to the point I
can't even get in via SSH. I've already used HTB/TC to reserve
bandwidth for my SSH port but the problem now isn't an attack on the
bandwidth. So I'm trying to figure out if there's a way to ensure that
SSH is given cpu and i/o priority.

However, so far reading seems to imply that it's probably not going to
help if the issue is i/o related and/or it would require escalating
SSH to such levels (above paging/filesystem processes) that makes it a
really bad idea.

Since I'm not the only person who face problems trying to remotely
access a locked up server, surely somebody must had come up with a
solution that didn't involve somebody/something hitting the power
button?

I would approach this issue from another perspective: who's locking up the server (as in eating all resources) and how to stop/constrain it. You can try to renice the sshd process and see what happens. I'm not entirely sure what 'locked up' means in this context.