Cheapest?
No.. to be the cheapest you'd start with a pinstripe and a het axanthic.
Quickest?
No.. to be the quickest, you'd want to have a good shot at producing one in your first generation of breeding
Best?
Quite possibly! I like your plan you've outlined here. You have a solid goal, and the entry cost isn't too high, and you won't be breeding for 4 generations before hitting it (hopefully).
I'd suggest starting with an axanthic female if possible, since a male pin het axanthic offspring (should you be lucky enough to hatch one) could feasibly breed the following season.