Status update: Abusing a PoE transformer for a high-voltage supply isn't exactly a good idea... Its low primary inductance (~3 μH) is indeed a problem, as expected - very little energy can be transferred in each flyback cycle, I got only 600 V max even when running it near saturation. #electronics
Found another AC/DC transformer model to abuse, it finally reached 1000 V. ⚡ Time to upgrade the impulse generator for switching 1 kV as well. #electronics