2 EU2000i's would be the way to go I think, for you. Yamaha has a interesting item, but I'm not sure if it would work.
Maximum AC Output3000 watts + 500 watts boost
Yamaha Boost Technology® (YBT) — Boosts output by adding battery voltage to alternator output when needed. The Boost Control Unit (BCU) senses when extra power is needed and boosts output for up to 10 seconds, giving air conditioners, power tools, and other equipment the extra boost of power they may need to start quickly and efficiently