Here's an update after purchasing a hdmi to DVI adapter:
I was able to view my computer through both monitors (TV and Dell monitor), however I can't unplug the CRT monitor without losing video on my TV. It's still seen as the "primary" monitor even though I switched it to the TV. I've tried restarting the computer with just the TV plugged in and video does show up until I get to my login screen. At that point my TV goes back to "no signal" and doesn't recognize the computer.
Although this could technically be considered "solved" I would like some more input to see if there's a better solution to this. It would suck to have to carry around an ancient CRT monitor with a nice TV.