How many amp draw do you have your inverter/charger set on? I always set mine a max of 15 amps to charge the batteries, then lower it to 10 for watching tv. No need to have the inverter inverting as you're getting 110 from the generator.
My Honda 2000 uses about a gallon every 5-51/2 hours. The Onan 7500 uses about 1/2 to 3/4 gallon per hour so Honda is much more efficient.
What I do is run the Onan while brewing coffee, hair dryer, toaster, etc and it Will handle all the big draw stuff and charge batteries, but after about an hour shutt it off and run the Honda on Eco mode with the inverter/charger set at 10 amp max until float is achieved.
You can run the inverter/charger set higher but it dramatically affects battery life.
Hope this helps.