Don't expect to find a more "modern" gasoline RV generator with "Eco" mode and reduced idle speeds. Even Honda's RV generators (as opposed to portable) are constant speed.
There is a reason for this, RV onboard generators are primarily used to power air conditioning, and a "constant" speed generator uses rotational energy to handle the surge of A/C compressor startup, slowing slightly to give the engine time to power up for the load. An inverter genset running reduced idle simply has no energy source to supply that surge of power (which might be 3X to 6X the rated output), which is why Honda tells you not to use Eco for air conditioning.
Some high-end RV/Marine gensets, all diesel that I know of, have inverters, but the inverters are rated for the A/C starting loads, and some are part of a hybrid system that stores electrical energy in a battery bank to provide the surge of power that the engine cannot supply until it spins up.
So you have essentially given yourself a set of rules that say you will not use the on-board genset in a low-cost motorhome.