Yes....and no. The issues with pre-engagement will still be there if the gears are cycling too quickly, adding a delay to it won't help.
In answer to your "what should I use" question, have you actually tried it with the stock gears and the 11.1v battery yet? Do that, swap the motor for the brushless and try it again. If it's still not quick enough, try a set of 16:1 gears (preferably a decent set like XT or SHS). Make sure you shim the gearbox properly or you risk it failing.
Don't just throw the bits all in at the same time because if you run into a problem, you won't know what caused it. Go slowly and change one thing at a time.
With the best will in the world, you are unlikely to turn a £150 rif into a £400 one by throwing loads of cheap parts at it, but you will (hopefully) learn how a gearbox works and have some fun along the way. Just don't set your expectations too high and you'll be fine.