This is no simple project. Especially if you wish anything but a square wave output. There will be a custom transformer in the design, adding to the cost and difficulty.
I notice there is no mention of the battery source. Are you aware that current draw for a 12 volt battery source (assuming no losses) is 250 amps?
You know, businesses throw away computer UPS supplies on a constant basis just because the batteries have gone bad and when they price them from the manufacturer (instead of going to a proper supplier) they just buy new ones.
It might be worth time and money to call around to several businesses in your area and ask if they've got any old ones they're going to pitch but haven't yet. I got a 2 KVA one free for that very reason and have had access to a ton of the smaller ones for free as well.
Most operate on 12V to begin with and if the output isn't to your liking the transformer could be salvaged.
I recently received a pair of 1KVA UPS'es that were obsolete due to the RS-232 interface, along with the batteries being shot. The manufacturer of the UPS'es wanted $300 each for new battery packs!
After searching around a bit, I found better-than replacement batteries that would put them back in operation for $143 including shipping instead of $600+$$$shipping.
A lot of the more commonmodels use a 12V gel cell of around 12-14 AH which I can often find for under $17 each if I get the ones with the large 1/4" spade terminals while the same battery with the smaller terminals is almost twice that price. Go figure.
Too bad they're not really capable of cranking a motorcycle starter (nor handling their charging system) or I could use one in my bike when my current one gives up the ghost. I'm hoping that if I give it the same winter storage routine as I did last year (not a simple trickle charger) I may get another year out of it, 3 seems to be the max for small power equipment batteries.