Given that I'm trying to switch a component signal and an 800x600 SVGA signal, I don't think I should be having any problems. I'm not asking for much. It's not like I'm trying to switch a 1920x1200 signal here. That's got to be less than 30MHz, right? (I'm not 100% sure how to calculate the bandwidth for the signal)
Switching it electronically is really what I want, especially as the projector has a serial port control on it, so I can have the whole thing nicely automated.