What I was thinking is instead of "pumping" it, you'd be theoretically cocking it 3 times. Personally, I think it would make it a lot faster.
That's sweet... If it was mine, I'd put a light spring in the pump to pull the cocking/pump handle back in to place every time. I don't know why, I just think that'd be a convenient addition.
Interesting thing to consider, it would be nice to make the pump motion easier.
Even a powerful spring won't be able to pump it fast enough at higher pressures. It will just push on the pump and air will slowly leak around the o-ring. Trust me, it won't work.