https://www.boatandrvaccessories.com/products/powermax-pm3-75lk-75-amp-12-volt-power-supply-with-led-lightI run a 75 amper like this set to 14.4v on my AGMs from a B&S P2200.
It maxes out the P2200 at a measured 1700VA but the gen keeps running.
The Honda 2200 is rated a little higher at 1800VA so it would be perfect with this 75 amper.
The converter linked has the big advantage that you can set it to any voltage your batteries are specified for and change that voltage when it is time to do so (such as when they are full and you drop to 13.x), or you can just run it as a normal three-stage in automatic mode.