First off D1, D2 need to be 600V fast or ultrafast types, e.g. 600V, 1A, 50nS, or better, e.g. BYV26C or better, the FR107's are too slow and may overheat and die with time, better check em.
OK, most likely as you wind up the voltage, the turn on transient (dV/dt) provided by your igbt's is getting into your control circuit and upsetting things to the point where two igbt's are on long enough at the same time to short the bus and kill each other. Good idea to put the smallest fuse that will allow low power testing in line with your bus supply to hopefully prevent more blow ups.
Also put a 275Vac rated 1uF across each half bridge, short leads, to soak up some energy when the igbt's turn off.
Also you likely need a DC blocking cap in series with your transformer (a few uF, 275Vac rated for now for safety), if the PWM is a bit asymmetric due to interference the flux in your transformer can staircase and overcurrent your devices - hence the DC blocking cap.
To sort the dV/dt, you need to up your gate drive resistors to say 1k for starters, R1,5,6,7, put a reverse schottky on them to still give a quick turn off, this should get you up to 325VDC bus for no load on your transformer. Change R8,9,10,11 to 10k, or to 16V zeners, 1W.
When you get to the stage of running load (start at low bus volts again and wind up gradually) if the igbt's turn on too slowly and get too hot, you will want to trim down the 1k's to get a balance of heat and interference to your control.
When you are running load you will want some serious C on the 325 bus, e.g. 100 - 470uF or more depending on your full load rating.
Oh yes, put some 1uF MLC caps right across Vcc to gnd on all your IC's, short leads, and a 10uF too, amazing what a stiff supply to the control IC's will do.
Let us all know how it goes....! good luck.