The mechbox sticking is caused by the motor/gears coming to a rest while the semi-auto cutoff lever is in the open position, usually caused by you quickly pulling the trigger and releasing before the shot is complete. It's a problem mainly seen in V3 gearboxes.
Active breaking doesn't change this. A shot completion timer and/or microswitch will though. A mosfet isn't necessary at all for a semi-only DMR, but does make it simpler if you get a computerized mosfet such as the Extreme Fire Cheetah or Panther... as it only requires you modifying the wiring, not the selector plate, to get semi-only.
If you are worried about your gearbox lockups of this type, then you can wire in a separate button in parallel to your trigger (this applies to both mosfet controlled and standard wiring setups, although it is much smaller in a mosfet setup as it doesn't carry a large current) so that you can complete the circuit and fire a shot (this button would be full-auto only, however, if you have standard wiring, or anything lower than a computerized mosfet with a single-shot timer) in the event that your gearbox gets stuck in this position.
Sykinder's solution only works if you have a gearbox similar to a v3 where you can get to the anti-reversal from the bottom of the gearbox, such as in an AK or G36. And the solution is a solution to a "locked" gearbox (stopped firing mid-cycle, but don't have the torque/power to finish the cycle from a stop when you try to resume firing)... which as I understand it, isn't your worry, but rather the 'stuck' gearbox where switching to full-auto solves the problem.