One reason that modern marine
power inverters proliferate is because they will drive microwave ovens. I've been doing just that since 1985 when I got my first inverter/charger. A 1200 W inverter will drive the largest microwave on the market because a good 1200W unit will deliver peak power around 3kW.
A 440 Amp-hour rated battery bank should be quite sufficient to drive that load. I often microwave two large potatos for 8-10 minutes with a microwave that draws 1200W. Not much later I microwave other items to heat them up...no problem. Been doing that for years. The only caveat is that the battery resistance (not capacity, although related) must be suffidiently low so that the inverter input voltgage equals or exceeds 11 Volts at the end of the cooking
time. With a good battery bank the Voltage will be 12V under load even after 15min of continuous ON microwaving. If the voltage is not high enough the cook times get longer and longer.
It is normal when driving an alternator
while using an inverter for the engine
to load down, after all, that is what is called a supported system and the energy is coming from the engine. With a good system no harm is done. Same thing would happen if the engine is working while you use the windlass
to get the anchor
up with a minimum retreival time due to higher operating voltgage.