Another converter topology to consider...
So, what do you think? Is this something that will suit your needs and you think you can build? It is fairly complex, but offers excellent performance and is standard in industry for DC to AC conversion at very high power levels. It is silent, light (relatively), and go up to 10+KW.
However, after thinking about your request for a while, I believe there is a much simpler way to achieve your goals. Attached is another circuit diagram that is much simpler, can be scaled up to 600/800W, 220VAC as you requested, but is noisy and less efficient. This schematic is a 150W design, but, like UPS systems, can be scaled up into the multi-KW power levels.
To scale this supply up to your power levels, you'd need about 6 MOSFETs per switching phase, a FET driver to overcome the input capacitance of 6 FET gates per phase, you'd need a 220VAC to 12VAC CT (center tap - very important! It must have a center tap for a push-pull design), 50/60Hz, 1KW (or more) power transformer (can be IE type or toroid), and the necessary wiring, PCB, etc. You could also use 2 transformers rated at 500W each if you can't find one with a center tap. This could make the transformers cheaper and easier to get. Basically you'd run the two primary's in series (forming a CT) and the two 220VAC secondaries in parallel.
Basically all this circuit does is take the 12VDC from the batteries, "chops it up" (switching) at 50 or 60Hz (depending on your local power grid), and feeds it into the transformer's secondary. The transformer then, through magnetic coupling, transforms the low input voltage (at very high current) into your required 220VAC (at lower currents). But, because you are switching the 12VDC into a square-wave, the output signal is pretty noisy and requires some filtering. It's also a noisy system (you can clearly/loudly hear the 50/60Hz hum produced) but depending on the appliance you're operating, you may not notice it anyway.
Same precautions apply here. Use extreme caution dealing with high voltages. Also, on the primary side of the system, as well as the system I previously described, you are dealing with VERY (like 100+ amps!) high currents that will require very beefy wiring, super thick traces with additional copper wire added to support the currents, and lots of capacitance (like 100,000uF or even 1/2Farad (like a car audio "super-cap")/16V) to filter the 12VDC.
Same thing applies here also - if you're going to attempt this project, ask lots of questions on this forum and document your project as you go so that you don't make major mistakes. There's no shame in asking for help. You can be more proud of a successful project that works and you asked lots of questions than to not ask questions and your project blows up in your face or destroys your microwave.
