Have the action timed and trued from SSS when you are ready to replace the barrel. It all has to come apart anyway to do it, and SSS will also true the barrel nut. And I would recommend one of their precision recoil lugs as well.

The stock can be swapped at any time, and I honestly do not see how taking it out of a factory savage synthetic stock and putting it into an XLR could make your accuracy worse. It should do nothing but make it better. It may not look right with the small barrel right now, but you'll be changing that anyway.