How to suppress current spikes in transistor feedback loop
I gave up dealing with transistor capacitances and found a much easier way to solve the problem: 



The circuit works by a very simple feedback loop: The current through the load is measured over Rshunt and fed back to the opamp as I*Rshunt, and thus regulating the output voltage. The LTC6255 is a good match for this application as it has limited slewrate (1.8V/us), and is therefore less prone to overshoot at rising edge. 



Perhaps this can help others with the need for fast regulation of capacitive loads with small currents. Note that the rising edge will due to the limited slewrate have a lower slope when the load goes more resistive, as a higher voltage is demanded at the output. Replacing Rshunt with a PWM driven BJT will provide the same control of reference as with Q1 in the first schematics.