Essentially if you did this, you'd be hooking up 2 outputs together. This is a great way to have a receiver train wreck. Which one would blow first?
If one was always off when the other was on, it'd be risky at best. Plus, I don't know how kindly those MOSFET's would take to getting charged in reverse. Would that make the display blink?

It sounds like you need a different piece of gear in order to operate optimally. I wish I could recommend a good stop-gap measure but, the responses above should be good insight into the best plan of attack.
Good luck..