Dr peppers comment about using the multimeter was to use the CURRENT ranges. On the current range, there is a low value resistor shunting the multimeter leads. The purpose of this is to shunt all the current except that required for the meter movement. The only problem with his suggestion is that without some calculations, you dont know the exact value of resistance and therefore your CRO 'current' range will be uncalibrated. If you use a known resistor, your CRO 'voltage range' is converted to a known 'current range'.
You are trying to do some theoretical calculations and that is fine. With inductive circuits, if you try to get them to turn off quickly, they will produce a high back-emf which needs to be considered. The generation of this high back emf results from the self capacitance of the coil. The energy stored in the inductance of the coil (0.5 x L x I2) has to be dissipated to get the coil current to zero. With no 'snubbing', the energy will transfer to the self capacitance of the coil and it will do this at the resonant frequency of the coil inductance and the associated self capacitance. The energy will be stored as an electric field in this self capacitance, and the voltage will be (0.5 x C x V2) and the frequency of the energy transfer will be f= 1/2 x pi xSQRT(LC)
You are possibly looking at this subject just as a simple current fall in an inductive circuit, but it is actually a resonant circuit and it RINGS. You should see ringing and the ringing will decay. If you dont want ringing or a high back emf, then the trick is to force the current to decay through a reverse biased diode. This will force the back-emf to continue the current flow in the coil, BUT it will increase the time to get the coil current to zero. This slows the switching action and is bad for a circuit that wants, or needs, to switch off in a short time. In your post #1, you said you have a FAST pulse, but for me a fast pulse is 10 nanoseconds. For a diesel motor, I reckon a fast pulse would be about 10 microseconds or more. So even with basic equipment you should get good results.
hope this helps.