Charge Pump-Based Gate drive supply
Let's make a charge pump...



Voltage source V1 is a 12V 100kHz square wave.

"SW" is the SW node from your MOSFET driver, ie the source of the top FET.

This will charge the bootstrap cap of your MOSFET driver to about 11V above the SW node, so it should work.

Now, when the FETs switch, SW node will go from 600V to 0V (or the other way around) very quickly, so the flying capacitor C2, will source or sink a nasty current spike into the square wave generator output. I added D3 D4 and R1 to dump this into ground or into the 12V power supply decoupling caps. 

This means C2 should be as small as possible while still supplying enough current to the driver.

If the FETs switch frequently or at high frequency this will increase losses and pump charge into the 12V rail, possibly raising its voltage.

These issues have to be weighted against the alternatives, which are using a small isolated DC-DC converter to power your top driver, or use a PMOS for the top FET.