There are obvious gaps in your report; fixing them would be a good first step towards better understanding the problem. For instance: [2013-02-06 10:57:59 -0500] Andre Goree:
I believe this started happening after a recent update but I can't know for sure and I can't really reproduce it...
Give a window for when you started noticing the symptoms. See in /var/log/pacman.log what packages were upgraded then. Downgrade them and see if the issue persists.
Using another system, I'm able to telnet to port 22 on the "frozen" box (I run ssh on this box) but cannot get connected via ssh.
What does "able to telnet to port 22" means? Do you get the SSH banner? If yes, when is the SSH connection hanged/interrupted (ssh -vvv)? What do the SSHD logs show on the server side?
I'm not actually using this box as a production server, just as my main work desktop
So you produce nothing at work?
Any tips on things I could set up to try to capture some sort of output or perhaps a kernel dump (if it's the kernel crashing)?
How about looking at the system logs to see what your system was up to just before a crash? -- Gaetan