Need help choosing a brushless motor for heli

I have a 200 size fixed pitch heli (Walkera 4f180 to be exact) that needs more power. What I have in it right now is a 5200kv outrunner. It's dimensions are 23mm in diameter by 20mm tall. the shaft (and it's critical that the replacement motor have the same size shaft) is 2mm in diameter.

I don't know what rpm the current motor runs at (on 2s btw) but the replacement motor needs to be about the same rpm (or faster would be ok I guess) on 2s and I need approximately 30%+ more torque for faster pullout when I gun the throttle. Their is room for the new motor to be up to 27mm in diameter and as much 30mm tall. I only have one pinion option for it as absolutely no one seems to know what pitch the maingear on the heli is (it's smaller than 0.4 mod and I have a feeling I would have a hard time finding a replacement pinion with the correct size hole even if I did.

My problem is I have no idea how to determine if a given motor will do what I need? There are tons of little outrunners like this available but what to look for is a mystery to me. Would I look for a higher KV? is KV directly related to the can size or can a motor of a given size be any KV?

If anyone can help me understand how to pick one out or maybe make a suggestion I would be eternally grateful!