First figure out why the damage, and correct the source.
Then you could add an alum plate under a new base to make up for whatever was cut off, sounds like a little more material under the mast wouldn't be a bad idea anyhow. 3" might be a lot and would look odd.
The way we usually handle a problem is very similar to Sailingfool's advise. We cut off the bad stuff and have a new step fabricated that makes up the difference. Rigging stays the same lengths.
Do try to eliminate the cause of the damage which is always standing water in and outside the base of the mast.
Make sure the new step has a limber hole to let the water out and coat the step and the inside of the mast where they meet with grease or some kind of anti-corrosion compound.