I must be missing something
We have a 2013 378XL. My inverter is located above the propane tank as others have said. The fan in the inverter only runs (or hums) when it is supplying 120 volts for the fridge and the inverter needs cooling. It only operates the fridge. If you want 120 volts anywhere else in the coach you will need to be hooked up to shore power or have the generator running.
I only have two coach batteries, they are connected in parallel.
2013 Georgetown XL 378
2008 Honda CR-V