I still want to know if current is unbalanced. I assume this is three phase motor (is it?).
Let's clarify what you mean by "swapping motors/pumps":
You took motorA/pumpA and put it into piping system B and power supply B? (And put the Bpump/motor into A piping/power?) And the higher current followed the pump/motor?
If so an additional possible check would be to swap motors only and not pumps. If the "problem" follows motor only and power supply/pump/system are not changed then that is proof of the motor. Additional checks on the motor would be windings resistance check and winding insulation check. Also rotate by hand checking for roughness.
Also we made an assumption that the higher current was the abnormal one. It is probably the case if you have overload tripping now which was not tripping before under similar conditions. Could be confirmed also if you have the pump curve.
=====================================
Eng-tips forums: The best place on the web for engineering discussions.