Isn't that about as close to an open circuit as you can get?

Whatever the switcher is, for church use it needs to be as dead simple as possible. Either big knobs where you add labels naming exactly what you have there (that is, "AUX 1" won't do, but "LEFT COMPUTER" will), or completely bulletproof and always correct autoswitching.

This brings up the question -- will you need to cue or edit? Now a whole different range of products are needed.