The all story reminded me the example of grabbing an arrow with naked hands.
Because this is all about.
At the blowing fuses all that you can measure is actually a single current spike.
Which is meaningless as information.
The inrush current has a practical value as measurement, and also has duration much larger than a single spike.
Yes one oscilloscope it could capture the spike too, but even if it was possible to get a reading, still there is no value at knowing the max peak current.
The third way, is to study your source, the batteries specifications include information about their cranking Amperes.
If you become aware about the cranking Amperes of your battery, then all that you need are measuring instruments which are capable to handle it.