Re: How much "extra" accuracy package is needed...
If it was already a straight shooter, then perhaps just rebarrel.
If it was 2 MOA, then definitely have the action trued.
You'll probably be fine. But, he may cut you a deal if you get the action trued at the same time. Afterall, the rifle will already be completely disassembled and he'll be headspacing, etc.
In the grand scheme of things, now would be the time to have the action trued because chasing the threads on the reciever later means that you'll have to do a setback or worse yet, get a new barrel.
A good stock and/or bedding will go a long ways. But, you can do that latter and/or do it yourself with no penalty.
...same for trigger work, picatinny rail, optics, etc. i.e. you can always add those later.