Well be aware some of these units cannot charge the batteries and invert at the same time. Some inverters can pass through your generator power and supplement with battery, but not all. Additionally, some generators are too "dirty" for the inverter to even use.
I'd be tempted to hook your generator to a chargeverter (once back in stock) to directly charge batteries, and then use the inverter to run the loads. Granted that does cost more, but it may be worth it to do what it sounds like you're trying to do.
I'd be tempted to hook your generator to a chargeverter (once back in stock) to directly charge batteries, and then use the inverter to run the loads. Granted that does cost more, but it may be worth it to do what it sounds like you're trying to do.