Hi Gary,
After referring to your drawing in post #5 my first wild guess is that you are picking up ringing off the batteries. Less likely would be an interaction between coils either electrically or fields. Last possible is you are developing capacitance some where in your circuit possibly in the windings.
It might be helpful to know the exact points you were probing for each display, but honestly probably wouldn't change my guesses.
I am not really much help just throwing some guesses out there.
I believe the triangular diagram you showed is supposed to be a representation of total input current vs total output current as a relationship and not necessarily what you would see on a scope even with a current probe.
Michael