Okay I've got TRIXX working for both video cards now. However, I still can't seem to actually mine with the second GPU, even though the system recognizes it and TRIXX allows me to tweak it. GUIMiner has the same selection from its Device drop down list as before I added the second card, just the original GPU Is this because I have no dummy plug or monitor plugged into the second card? Do I absolutely need to plug one of those in before it will let me do any mining with the card?
Sounds like you're still on the older 11.6 drivers then. Yes either a dummy plug or an actual connection to a monitor is needed in this case.
Also, I have previous experience with Linux, although not very recently. I'd be able to get Ubuntu going (though I'm leaning toward Kubuntu - KDE seems awesome!) which will be ideal for me, as I'm looking for something beyond the basic command line setup.
To get the most out of your cards on a Linux system, you should run without X. The linux ATI/AMD drivers tend not to be as fast as the Windows one so every little bit counts.
Most of the things you would want to do on a mining rig would be through the command line anyway.