Well, an NMOS source follower isn't a current source so the results you are getting are the results I would expect. A PMOS connected common source can be a current source if you drive the gate voltage to the correct level (but the gate voltage logic would be inverted).
Is this for integration on a custom IC or to be made from discrete parts?
I am not sure what you are trying to achieve. Well, I can see the waveforms you want, but I am not sure why. Also, I don't have a feel for the voltages and currents involved i.e. a few volts or hundreds, a few mA or tens of amps.
Also, I guess, the speed involved. You mention 300us (not really "a very short pulse") but that would make the period of the signal in the millisecond region, I would have thought.
With a bit more information I will try to help.
Keith