A combination which has given me very snappy trigger response is a very high torque motor (eg: any ACM neo motor with a high number of winds like the JG Blue, or anything labelled "infinite torque up" with strong neodymium magnets) combined with high speed (15:1 or 13:1) gears. Your high torque motor will reach its maximum speed quicker than a high speed motor. If you do everything right, you can easily still achieve a nice high rps with this, even with a 7.4V LiPo, without crazy heat.
As you partially noted, you can reduce stress on the gears and motor by using a weaker spring, better shimming (and
better contact between gears), better bushings, grease, etc, but also, you can use a more powerful motor with neodymium magnets (like the JG Blue).
One notable thing that's missing from your list if you intend to use a 11.1V LiPo is a MOSFET, which you will definitely need if you do not want your trigger contacts to go nuclear.
Personally, I don't think you absolutely need to go with an 11.1 until you've exhausted all your other options in terms of reducing friction and getting a more powerful/efficient motor. If an idiot like me can manage 20 - 25rps with reasonably strong springs on 7.4V batteries and good trigger response, anyone can
