k7elp60 Has the seed of a great idea! Get a small inverter with a capacity of maybe 240W. This usually consists of a simple regulated 12V to 165V boost or flyback converter connected to an H-bridge that makes the 50/60 Hz.
Tear out the H-bridge and change the regulation to 85V instead of 165.
IF you charge the batteries in parallel then this is very unlikely to happen because the batteries will become balanced.
A flyback topology will be much more compact because the duty cycle on the primary can be lower to get the same voltage increase. A autotransformer will give you a small reduction in size and cost.