OK - finally got a chance to see the drawing you posted. Yep - That's exactly what you want to do. So you can either buy a parallel switchbox that switches all 25 lines, or you can gang a bunch of relays together and switch just the lines you need.
As for the auto-switch from Belkin - I don't think that will work. It's designed to switch based on a signal from the host machine. But the signals from your controllers (either the DMX board or Norm's DAC) are both going to be on, so which one gets the port? Then too, the signals are totally different, and they're on different pins too. So no, I don't think that's going to work...
Adam