My PHD is the opposite, all kinds of complexity and experimentation, I have trouble keeping him to simple ha ha!
He would have used a scope in one shot mode to see the current waveform and precisely see the peak current over time.
No meter is going to give you a good idea at all for something like this, but different strokes for different folks, mine is more in the RF side, and that stuff is black magic, ask any electrical engineer.
Anyway, it sure seems you will have no choice.
Greg