Ok guys. I just got done with a week long dry camping trip so now I can give better details. Here is the inverter I bought. Link
I never got to really test the inverter until this trip.
I got to my site about 1:30, set everything up and then ran the genny from 5-9pm. At 9pm I switched to my inverter and watched TV until about 11:30. I also had my phone charging, a laptop plugged in as well as an FM transmitter plugged in. The microwave, AC and electric water heater breakers were shut off. Fridge on gas. I only used one or two lights from about 9pm-12 and they are LED panels anyway. The water pump was used sparingly for 2 flushes and to brush my teeth.
I woke up around 7am and my dual battery setup was reading 1/3. My batteries were fully charged since the camper was plugged in at home before the trip and then I had the genny running all evening too.
Over the next 2 days I didn't used the inverter at all and barely used the batteries at all since I was at the beach or at another camper. I was charging the batteries for around 6 hours each day.
One night after the genny hours ended I hooked the inverter back up but this time I switched off the converter breaker. The only problem with shutting that breaker was that it also cut off power to the living room and bedroom outlets since they are on the same breaker as the converter. I still has live outlets in the bathroom, kitchen and outside though.
So from about 9pm-7am I used one or two LED light panels at a time, the TV and radio for a bit, the water pump for a flush or two, the inverter, and also had my phone charging. When I woke at 7am the battery gauge was still reading full.
I used the inverter with the converter breaker switched off for the next few nights with the same result, batteries full when I got up. The converter was clearly the power hog which I had already known going into my test.
Once this season is over I'm going to see about permanently installing the inverter in the camper. For this trip I only placed it on top of the batteries when I was using it. I'm also going to see about installing another breaker in my panel so the converter and bedroom/living room outlets are on different breakers.