Transfer switches are basically just 2 relays or contactors set up in a way that only one can run at a time.Having both "lines" at the same time is impossible.Why would you want to change it if it works?
Battery has nothing to do with this. You either have a 12V load that is too high or your converter is having problems.Also your battery is meant for travelling and short term power. If you have a battery disconnect, I would recommend shutting it off ...