High Current Pulse Opamp 2.5% Duty Cycle
Power supply current-limiting may not expect fast transient events at its output terminals - a good one should switch from "voltage output" mode to "current-limited output" very quickly (to protect the load), but many take some time to switch modes and stabilize. Some switch back to "voltage output" mode from "current-limit" mode much more slowly - this could be your problem. Power supply spec sheets often don't characterize transient response of mode-switching.
The solution that some have suggested adds a series buffering resistor between DC supply and the large reservoir capacitor. This resistor should be large enough that the average current drawn from the supply doesn't invoke current-limiting, in an attempt to avoid mode-switching transient issues. This solution does soften the DC supply regulation, so you need a bit more voltage going in. And this over-voltage becomes dependent on duty cycle (150us/6ms).
If you really trust your op-amp/MOSfet current regulator, invoking your DC supply's current limiter is redundant protection, and shouldn't be necessary. But be aware that some DC supplies just can't handle fast transient events - internal regulation can go crazy when driving pulse loads, especially where some inductance exists between supply and pulse circuit. (You might try twisting together the two supply wires between load &amp; source).