[Al Skierkiewicz]

Z,
Some of the items you mention are due to the power supply you are using. The motor testing needs a very high current, low impedance supply to obtain accurate data. It is not possible to measure motor current directly as the polarity at the output of the device changes. While possible with multiple INA193, it raises the parts count per device. Measuring input current is affected by device current demands but these are low compared to the motor current. Jaguars rarely reboot in the field although they do fault on low input voltage.
You do not mention what throttle value you are running the motor at but it appears to be something much less than 50% duty cycle. So what comes into play is the brush spacing and the motor rpm. So current draw is reflected by the number of commutator segments that are in contact with brush at any one time. This is common for brushed motors.
If your power supply is really sagging during high current pulses, then I would expect the output of the INA193 to also reflect that. It is internally referenced to the power supply input pin. It might be interesting to add a trace of the power input voltage with the other waveforms. The triangle waveform is a result of the inductance of the motor windings interacting with the current input. At 15kHz this has a smoothing affect that many believe gives the Jaguar it's more linear response. It is the Victor that is switching at 150 Hz.