question

The Multi 3000 will charge at up to 120 amps into 12 volts. That matches the propane output of the Champion you suggested. I don't see a need to lug around anything larger unless you are camping at higher altitudes.

Generator output decreases roughly 3.5% for every 1000 feet above sea level, and for gasoline, you may need to change carburetor jets at some altitude. So at 5000 feet, you loose 18% or a max of about 1200 watts running on propane. You'd want to set the input current limit to 10 amps to avoid overloading the generator. Of course you'll need to increase your charging time too.

Your battery bank may have a lower maximum charge current and may need to factor that into system setup.

In order to figure out how long you'll need to run your generator each day and/or figure out how often you'll need to run it, you'll need to do some simple math. Take stock of your consumption in terms of watt-hours per day. For example, if your fridge consumes 200 watts and runs 50% of the time, that's 200 * 0.5 * 24 or 2,400 watt-hours per day. Make these same calculations for all your loads and add things up. If your loads total 4000 watt-hours, you'd need to run a generator 3 hours at 1400 watts to recharge the batteries plus a bit for cell balancing (absorption phase) at least once in a while. Your battery bank is good for 3300 watt-hours but to be safe you should only use about 80% of that or 2,700 watt-hours usable. That says you'd need to recharge your batteries every 16 hours.

These numbers are only examples. Make your own consumption calculations to see where you stand. Make sure you include your 12 volt loads in the calculations!!!

There is also nothing wrong with running the generator while you are inverting to feed your loads. With a properly set input current limit, the inverter will pass generator power to the loads up to that limit and combine that with power from the batteries to satisfy heavy loads when needed. When loads are less, the charger will kick in.

Make sense?