This might seem odd but how about a new microwave? Panasonic makes an inverter model that actually uses a lower power level when directed vs most that cycle on and off.
You should be able to run on level 4 or 5 with your existing Honda 1000. Of course full power if you have full utility power. Lots less money than a new Honda 2000.
Member 'full_mosey' has one and works on his 1000 watt inverter.
http://www.rv.net/forum/index.cfm/fuseaction/thread/tid/28241998/gotomsg/28244226.cfm#28244226Panasonic Inverter Microwaves