Even though the switch box states that it is for 1 amp switching between 2 (or more depending on which switch box you buy) sets of stereo speakers, since internally there are only mechanical gates opening and closing, you should be able to reverse it: connect your amps to the speakers posts and connect the speaker to the amp posts. Same principle: gate A closes and the signal (direction is irrelevant) flows from the amp that is connected to the gate A posts to the speakers connected to the amp posts; the same for the gate B amp.
Buy the Bryston Switchbox from someone like AudioAdvisor.com and you can return it within 30 days for a full refund less shipping. And you can test it.