Cool idea. Never had one so I just ordered. ThanksAs mentioned above the item linked below is a good low-dollar investment for boat owners with multiple batteries.
This will sound silly...but have you checked around for a fifth battery? On the floor between the engines possibly? Any other spots that could hold a battery dedicated to the generator?
https://www.amazon.com/gp/product/B000AMBOI0/ref=ppx_yo_dt_b_search_asin_title?ie=UTF8&psc=1