Hello there, if you have 4 batteries at 12V each, why not put them in series? 48V to step up to 310?
At 5kW out, you will be drawing >105 amps from the batteries. Unless they are >500Ah, they will not last long...!
So you could have 3 interleaved boosters each drawing 35A (+ a bit for losses) at 75kHz each say, 120 degrees out of phase so that the current drawn from the batts looks more like DC, (and easier on the o/p caps - by the way the o/p caps will need to be close, low ESR/ESL & high quality!).
This could actually be made to work, we have designed similar boosters for solar power systems, good luck!
Regards, Anna.