2x 6V golf cart batteries wired in series. These are TRUE deep cycle batteries, not "dual purpose". They store a lot of energy and handle discharging and charging better.
Get rid of your existing converter and replace it with a combination inverter/charger/automatic transfer switch. Easy to install
(hook you DC fuse/distribution panel directly to the battery bank). Even easier to use
(it will charge the battery back when shore power is available and automatically switches from shore power to battery when there is a load).
Buy a GOOD battery monitor like a
Victron BMV-700.
If you don't use the coffee maker I am certain you can get by with less than 1 hour per day on the generator. If you want the automatic coffee maker and a toaster, you will have to fire the generator up shortly after breakfast. Worst case, run it a second time before evening until the battery monitor says the battery bank is full.
If you are going to be travelling a lot, I strongly suggest a DC-DC battery charger. That way even if you hit the road immediately after breakfast you can be sure the batteries will be fully charged.