As for the reset not resetting the shot count: that would be too easy!
Also idea for a power up if you're so inclined: when you get a hole in one on normal mode, visualize the gravity wells for the next level or two.
I like the ghost arrow idea a lot - I'm thinking of adding that to hard mode.
Another suggestion: replay shot.i just had a hilariously roundabout hole in one. I wish i could replay it to grab a video to share (and therefore advertise your game!)
As long as the simulation is deterministic you'll be good to go.
Given a level and a list of velocities any sequence of shots should be reproducible.
As for the reset not resetting the shot count: that would be too easy!