Thanks for all the advice. So I'll go for IGBTs.
What properties should I try to match as close as possible, and which are OK to go over (and by how much), or go under?
(Except the obvious: Collector-Emitter Breakdown Voltage (Vces) / Current - Collector(Ic) / Pd - Power Dissipation.)
Also, my IBGT is a 4A part, but many of the options I found are 10-30A. So the required saturation values could probably be less when replacing a 4A part?
For my part (also attached datasheet), these are a selection of values (maybe others are needed too?):
| Property | min | typ | max |
| Vce Saturation(VCE(sat)) | 1.7V | 2.0V | 2.4V |
| Gate-Emitter Threshold Voltage (Vge(th)@Ic) | 3V | 4V | 5V |
| Gate Charge(Qg) | x | 24nC@15V | 31nC@15V |
| Input Capacitance(Cies) | x | 264pF | 317pF |
| Td(on) | x | 22ns | 26ns |
| Td(off) | x | 237ns | 284ns |
| Turn-On Energy (Eon) | x | 0.070mJ | 0.081mJ |
| Switching Energy(Eoff) | x | 0.061mJ | 0.079mJ |
| Reverse Transfer Capacitance (Cres) | x | 17pF | 20pF |
Also, the symbol in the datasheet doesn't show a body diode, but the text says:
"Energy losses include “tail” and diode reverse recovery."
Can I assume it has a body diode? Since many of my part options show a diode in the IGBT symbol in the datasheet.