You could switch batteries. A DPDT switch would allow you cross the batteries between two SkyViews. I don't see why this wouldn't work, although SkyView will likely reboot if you throw the switch while SKyView is running off batteries.
I think you are making this awfully complex though. The battery in SkyView lasts at least an hour. Half of that draw is the screen, so if you dim the screen you can likely make it two hours. If you have two screens on at once they will even last a bit longer since they share the load of units on the network.
It seems to me that if an alternator failure is a critical problem when you are flying, that you can get down within an hour. Adding complexity to deal with the corner cases often has unintended consequences and adds to pilot workload in already stressful situations.
The design goal of SkyView was a system that had absolutely zero degradation in performance for one hour after electricity failed so that the pilot had no partial panel stress with an electrical failure. We believe that the hour is a very long time to get the airplane somewhere safe.
If you really want more than an hour, you might be better with a larger lead acid backup battery that the pilot manages if the alternator fails.
