I did some tests to simulate the possible overshoot using a DCP405 and driving the prog of it with a signal generator and an on-amp configuration like the design.
The AWG starts at 0V then generating a short pulse at 2.5V (full scale of rprog, rise time = 9ns) and after that it goes down to a lower value simulating the situation where the rprog is driven at a step of 2.5V and there is a limit set.
I varied the voltage levels, the length of the pulse and the load of the DCP405:
- The load doen't change things as long as the current limit is high enough.
- The worst case seems to be a low limit value and a full scale (2.5V) step. Seems logical..
- Worst case meaning the settings where the shortest pulse width created overshoot.
First I played around with limit around 1.25V (20V output). A pulse < 100us didn't give overshoot.
Playing with low limit values (around 1V) make things a lot worse:

This is with a pulse of 20us at 2.5V and a limit voltage of 100mV (output = 0,7V)
Decreasing the pulse with to 10us gives:

Going even lower (limit = 70mV / output = 0,2V) also gives overshoot at 10us, reducing the pulse with 8us eliminates this also.
This is a pretty extreme edge case: You set the output limit to 0,2V and drive the rprog interface to deliver 40V...
The most extreme overhoot (relative) is to step 8mV into rprog with an offset of 57mV (= 0V output in my setup), still feeding a 2us 2.5 pulse, then 8mV causes a output of overshoot of 100mV at 120mV. It is a very extreme case: who will set the limit to 0.1 V?
Given the specs from the datasheets of the comparator and logic this should not be a problem. The comparator is max 2us and the logic is an order of magnitude below that.
I think the limit circuit is fast enough for the voltage control.