the vertical axis wobble is indeed the intended input mechanic. the critical observation to make I would hope is that it allows you to decouple the gun orientation from the head orientation, so that you don't have to wave your camera all over the place just to shoot. instead, you can focus the camera on your intended target, and then swing the gun 'through' it, while staying 'aimed' at it the whole time. the purpose of RMB is to stabilize the gun before and after the swing, but not during.
I believe this is reaching the limit of my ability to describe these things in words :) and I realized itch allows you to embed gifs, albeit at terrible quality:
it's quite possible that the sensitivity of the flicking action is just too high by default.
your comments on incremental level design are accurate and incisive.
and yes! catching bullets is a thing. however, it's much harder to do than dodge, and we didn't have time to implement a useful reward for doing so.