So you have it working and putting out a pulse every N pulses, and the current problem is that you can’t stop it from repeating.
Thinking within the context of a custom unit here:
You could put a linear VCA between the incoming clock and the count unit, and use a copy of the count’s own output to close the VCA - shut off the incoming clock. And then use a copy of the same signal you’re sending to the reset to re-open it?
I haven’t worked this out yet and not 100% sure it can be made to work. Just thinking out loud the direction I’d start heading. Some S&H or track and hold might be needed?