I've set up the exercise bike in front of the new TV, and hooked one of the spare PCs up on it. I got a Logitech cordless rumblepad to control the games. This is the cordless version of what I use for playing poker on my desktop computer-- I have macros set up to make it work well, and playing with it is now second nature.
Tonight I got everything in place and hopped on the bike for a test. I decided to do something brief just to make sure everything was OK-- in this case, a couple of orbits of two low-stakes ring games.
Results: it works. I need some sort of small waist-high side table for the keyboard and mouse and a glass of water, but that's a small optimization. I easily pedaled away for about 15 minutes without losing my focus on the games. Win!