'
The barrel threads on the Number 1 or Number 4 rifle are too small and would have to be cut off. Then, you still have a barrel that has a flat on top (the Knox form) and a very short tapered area. The bolt face would have to be opened up to accommodate the .303 case rim and the barrel would have to be rechambered. Add to that, the problem of getting the rounds to feed, and you are really into big $$$$$$$$$ for something that would not be that suitable or reliable.
If you want something in the AXIS line, why not simply buy a 30-06 or .308? You will be much happier, because to do what you asked about, even if you could find a Gunsmith that would do it and guarantee that it would work, would probably cost you twice what a new Savage Axis would cost.