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Jeff, ac or dc, 12 volts or 120 volts, really isn't significant here. Yes, there are some differences. An inverter may waste 10% power as it operates. And 220vac appliances may be more efficient than 110vac. And DC systems need charging, which always requires more power than it stores. There are pros and cons to all of them but I suggest the only thing that matters in your situation is WATTS.
You want to run a 950 watt microwave, which probably consumes about 1200 watts on the innput side to have that much output. Watts will be watts (not really, but close enough) regardless of AC or DC.
1200 watts from a 12 volt source will pull 100 amps, maybe for two minutes warming your coffee. Twenty minutes cooking dinner. That's something like 200 amp-minutes for the coffee, 2000 amp-minutes for dinner. Except we talk in amp-hours, so we divide by sixty, the coffee needs about 3AH to get heated, dinner needs about 33AH.
Your two group27 deep cycle batteries (and you want deep cycle, not SLI) might be rated 100AH each, although 80 is probably more realistic. You don't want to cycle them below 30-50%, so using the two combined, you can draw about 80AH before it is time to recharge. Or 40AH is you don't combine them and alternate them.
Nuke two dinners, and you have to recharge. Or...just run the engine and alternator to power the microwave. There are just limits to what you can do with a small powerplant (engine, battery, quantum reactor, whatever) and ac or dc won't make much difference in that.
Yes, DC appliances work. Take a second look in the truckstop, see how many of those brands are featured on the PBS cooking shows. They may not rival the quality and features of 110 appliances, but you don't see many skinny truckers out there, they must be cooking on something, huh? :-)
Either way, you'll still need to make and follow an energy budget. Reheating coffee is best [not] done in a good Thermos. And those $20 single-burner butane stoves you can buy in any dollar stove, are quietly being used in an awful lot of boats.