Filtering Voltage Spikes on Split Power Cable
It looks to me that your suspicions are right, as are your possible solutions. You can try adding a decoupling capacitor placed as close as possible to the load points, in that way, the disturbances in the load are absorbed by the capacitor and do not propagate through the cable.

It can be a "not big" capacitor, you can try a ceramic or plastic capacitor, if it is too small it will have no effect, if too big it will be a hard load for the supply, since capacitors behave like short circuits when they are discharged.

As you commented, you can also add a ferrite bead. As the capacitor, it should be as close as possible to the load causing the disturbance (but not closer than the capacitor). If it is difficult to put the bead because of the connectors, you can try hinged ferrites.