Hi,
Another option to consider is a Victron Energy Multiplus inverter/charger. This is an interesting unit if your not familiar with it. Using an external control panel, you can control and limit the Multiplus to accept the amount of input current that's available (genset or shore pwr) from 0 to 30 amps. A Honda 2000 can provide about 15 amps if I recall. What will happen during an A/C unit startup is the inverter side will parallel with the input current side to provide the necessary extra inrush current beyond 15 amps to allow the A/C unit to start. Once that load backs off which, I think is below 15 amps, the Multiplus will shift to charger mode and use whatever available AC current is available to recharge the batteries with - all automatically.
On our previous boat, we had a 3000VA unit which, worked like a charm, with a 5000btu A/C unit and a Honda 2000 generator. I'm in the process of installing a 2000VA unit (the stock inverter died) on our R27 which should work fine with the Mase genset that is supposedly sized to handle the A/C start loads. I should mention that the 2000 VA unit can provide up to 80A of charging current which, I look forward too over the 20A stock charger. I will also mention I located the new 2000VA Multiplus to the 'cave' to give it half a chance to survive vs. the 'wet locker' where the stock inverter was located.
Safe, happy voyaging folks.
Ken
2014 R27 O'Meara