The simple way to do this would be to just go out and buy a little 300 watt inverter, even a little 300 watt UPS (Uninteruptable Power Supply) could be easily hacked. These are typically 12 VDC to 120 VAC and then place a full wave bridge rectifier on the AC output and filter as required. A simple cheap UPS can be had for less than $50 USD exceeding what you need. Place the 12 volt batteries in parallel. My thinking is it cost less to buy than build.