(1) Thanks for the writeup, this is classic HN content, a simple app that solves a person's problem with enough interesting technical detail to make it interesting.
(2) Definitely post this to the App Store! I'd happily pay a few $ for it even.
(3) How would it handle burpees? Would it just ignore the 'jump' phase? But still count the push-ups since it's zeroed in on the up/down motion of the push-up itself?