I agree that you should work through this from the direction of least invasive/least expensive answers first, then head to the bigger fixes. I'd upgrade the bases/mounts, preform a thorough cleaning, then go shoot 3 groups through it.
If there is no change to the grouping I'd head to a smith for stock work or do that yourself. If you end up at the smith also ask them to take a look at the bore, crown, and bolt for possible contributing factors. If nothing is apparent then start with the work on the stock and go shoot some more groups. If you are still unhappy go back and get the action and barrel work done you would like. As much as I like the AI, in your case of not handloading I would stick with the more readily available 280 rem chambering. It really is a beautiful rifle with well placed sentiment. Don't sacrifice the sentiment to make another long range rifle in the safe.