Ok now I'm the one being dense. I'd figured out using the clutches with a shaft junction, but how would you get a multidirectional clutch to switch inputs on redstone instead of outputs?
Yea, multiple input clutches IS how you switch the input. They do indeed have only 1 input each, and can only toggle the output. Basically, you put them on the input line, and then you are toggling them on/off. ( Well, you could get really technical and redirect them and still put the power in. )
And now you're thinking like an Engineer. And Cave Johnson. But he's crazy. I mean, Science is about nothing BUT why! Engineering? Oh, that's all "Why not?" the whole way down.
That's why I said if you really wanted to, not "but that would be stupid"
However, I disagree that science is about nothing but why. Science is about everything, in every way shape and form.
I find the better question to express engineering is "How?" Of course, "How" and "Why not?" often go together, I just find the how is more to the core of what engineering is. I also think a good one for science is, "Wait...what?"