You have, as you say 144 amps rms in the igbt's, this is 203 amps peak, + a bit of ripple, so 250 amp IGBTs is a good safe figure to settle on. In a 6 switch (3 phase) bridge the average current per device will be less, which allows for better thermal performance of each device.
There are many makers of IGBT's, powerex, semikron, IXYS, being three reputable brands, no doubt a thorough web search will find a maker or distributor near you.
Regards, Orson Cart.