Too many unknowns to give you a specific answer.
Shop for a combination inverter/charger/automatic transfer switch. All of the good quality ones do "smart charging" and have settings for flooded (wet) or AGM lead acid batteries as well as lithium. Better ones actually have an input for a generator.
If you get the combo I suggested, start by removing the old converter. You want your new inverter/charger/automatic transfer switch located as close as possible to your batteries. Wire your DC distribution panel directly to the batteries (via s mega-fuse) and an ampere meter shunt). Your outside cord should go directly to the new unit. The output of the new unit goes to the AC breaker box.
