I must have misunderstood this response.
...
No, chalk it up to my casually mentioning a few points at the same time, which is a bit fuzzy.
Re what I said at the bottom;
"Also the integrator does not need to be THAT big, it just needs to have a response time significantly slower than the control loop response and slower than any regular noise ripple etc on the feedback signal."
The important bit is the integrator needs to be big enough so the FETs remain at a constant bias even when the target PSU has ripple, the last thing you want is the FETs trying to switch themsleves on and off to respond to PSU ripple and mains ripple.
Normally I would have the time constant on the output integrator slow enough so it won't be responding to 100Hz or 120Hz mains ripple on the target PSU. The opamp itself will respond to the mains ripple and vary up and down at 120Hz (maintaining an average FET bias) but when that is happening the voltage on the FET gates should ideally be DC, so they act like a massive power resistor of a fixed value, giving the correct average current even though some ripple exists on the target PSU.
If you wanted to add that load on/off switch, it can be added as part of the integrator so it cuts the voltage to the FETs base. So switching the switch on will ramp the current gently up to max, switching it off will ramp the current down to zero. (Assuming both target PSU and opamp PSU are running).