Thanks so much for the replies and info, everyone. Sounds like the first thing to do is nail down the 'starting' wattage of the microwave, to determine just what sort of beast I'm trying to deal with. The local library lends out Kill-a-Watt meters that will do this work for me; off to the library!
I'm not sure the power consumption calculation is as straightforward as majaross worked out. On the DonRowe site that gbaglo passed along, there's a basic calculator for inverter runtimes from batteries:
Another forum is grappling with a similar challenge, though these guys have much bigger RV's:
I'm also not concerned about frying the wiring in the Escape. I recently rewired a '76 Trillium from scratch, so am familiar with DC wiring. I'll not be tying the inverter into the 'regular' AC system; rather, I'll completely isolate the inverter behind the appropriate DC fuses (at the battery), and run dedicated AC wiring to new receptacles for inverter-based power.
At least, that's what I have in my head right now....