[Al Skierkiewicz]

Z,
The specification on your power supply states a 35 amp max output at 12 volts. The CIM motor has a 130 amp stall current. It will draw 130 amps when starting limited only by the wiring and the series resistance of the controller. At lower throttle values I would expect that the power supply is likely going into current foldback during the "On" period of the output waveform. The current waveform is exactly what I would expect under those conditions. Perhaps Rich Wallace will weigh in. He has done some measurements using a industrial motor test facility. I seem to remember a 1200 amp power supply with impedance control but I don't know if that is his setup.
When the Jaguar or other controller is in the brake mode, two legs of the bridge are turned on to simulate a short across the motor, that does not prevent some energy making it's way to the outside world through the power input terminals via the diodes in the FET devices.
Additionally the jaguar uses a particular gate driver chip that has a charge pump to keep drive high at low input voltage and also requires a bootstrap cap for the gate drivers. In order to keep these 3 caps charged up, the output switches independently of the commanded output. This is visible during "0" throttle (as a very narrow pulse) but may be harder to see at other times. If the driver chip sees less than ideal gate drive voltage, it reduces the output as well.