Passive ringing on PCB causing noise
Placing thick ferrite beads (even a multi-wrapped type) over the fast changing high current wiring (or component leads) can help absorb some of the power and should reduce the ringing. Even placing ferrite beads over ground wires (and conducting metal brackets) can sometimes help.

Can the PCB or other circuitry being affected be shielded with metal sheeting? Can the inductive component generating the signal be shielded?    

The fast changing current signal will follow the path of least impedance.  Can that path be altered to avoid having it pass close to the sensitive circuits? (e.g.: Move or change grounding hardware.)  If the high current path forms a loop can that loop size be reduced? (e.g.: Run wiring of all high current signals direct to their input point, then have the corresponding return wiring very close to that same input wiring.)