To amplify the current:
1. You'll probably need a better floating 12v supply for the high side, with some good surge caps.
2. You buffer the drive signal with higher current MOSFETS. Say 30v-50v/30A devices.
To avoid cross conduction:
1. You don't want cross conduction in the driver FETs and you DON'T want cross conduction in the IGBTs. The normal way is to introduce a delay for the switch on device that ensures enough time for the device switching off, to be fully off. Since turning on is from 0 to +12v you just need to delay that edge(you still need to cleanly switch this device,no long switchon), while not delaying the +12v to 0v edge. If you're driving 1000A worth of 1200v IGBTs, you should know how to do that.