Made a good deal more progress on getting my MythTV to work. Combining crap lying around my apartment with crap lying around Dan's apartment, I successfully got a PC together that works with the TV-out feature of the video card I picked up.
Got it hooked up to the TV and the cable box. Can now watch TV using this Frankenputer. The only real issue remaining is getting the IR blaster to properly change the channels.
Looks like the root of the segfault I was seeing over the weekend was in fact a result of running at 1024x768 resolution. I dropped it down to 800x600 and the segfault went away. So I successfully worked around the issue, but there is certainly something going on there worth looking at.