When I was debugging fast power FET circuits, I found that the 'scope would show a damped ringing during the circuit's transitions even with the probe connected but grounded to itself. This was due to HF common mode currents from the circuit passing thru the probe and scope. I could eliminate them by passing the probe cable thru a high mu common mode choke a few times.
Another use for a high mu choke is to use it as a pulse compressor or intensifier. The theory is to apply a voltage pulse to a high mu choke in series with the load. The choke's inductance will initially limit the di/dt to allow the switch to fully close. At some point the current saturates the core of the choke and it essentially shorts out and not longer limits di/dt giving a sharper, higher current pulse. If another parallel C and series L is added, the pulse can be further compressed.
I found this effect when performing ESD susceptibility tests on a product when a common mode choke saturated and passed an intensified pulse to the power supply which then glitched. I then found that this effect was used to generate narrow pulses for lasers and radar transmitters, far sharper and narrower than you'd think the switching devices would be able to generate. I found a few papers on drivers using this effect, but no tutorials on how to roll your own - an exercise for the student, I suppose. I've never tried to use this effect, so I can't give much direct advice. If memory serves, a 10 A pulse became a 30 A pulse with about 1/4 the duration.
Intuitively, it might help here because it could allow the IGBT to operate within its safe operating area by reducing Vce more rapidly during turn on, perhaps compensating for the Miller effect.
Cheers,