What do you mean by "whining post cycle"?
It's not a good idea running a normal AEG on 11.1V because it will burn the contacts on the trigger switch. Make a simple MOSFET circuit that protects it, then it should be fine.
However if there are weird sounds when using it, there is probably something else is going on with the gun. High torque motor will only make it cycle faster and possibly double feeding, plus since it will draw much higher current, it will burn the switch much faster.
All in all, if it is a backup gun, you might be better off with a 7.4V lipo and not modifying the gun itself.