"I'm the greatest gunsmith ever." -Just ask me I'll tell you...
Pretty much a statement that most shops tend to feel in the very core of their bones. Now temper it with this: You own a gun and it shoots well (I'm assuming as you made no statement to the contrary.) There's no reason to think it will suddenly fall off the wagon just because someone new hangs a different stick on it. FWIW the whole accurizing thing is a way to compliment a well running bolt action rifle. The nitty gritty of accuracy begins with a well made, well fitted premium barrel. All the lapping in the world won't put enough lip stick on the pig to make you want to sleep with it.
To pummel this further: It could be accurized/blueprinted/trued with an spork and a chainsaw. The end result on paper drives the boat however. So long as fundamental things like Primary Extraction, basic safety, etc were/are observed, there's no reason to think it won't perform to the appropriate standard. There's shops that absolutely refuse to install a barrel on an M700 that they have not worked over personally. I take a different tract by asking you how it runs presently. Assuming you say "good" or "gooder"

then who am I to shove another couple hundred bucks down your pie hole?
If
you are in doubt or concerned then do whatever it takes to make you feel good about the effort.
With that know when you bounce from 308 W down to a 223 Rem there's going to be more work involved. The bolt will either have to be heavily modified or replaced. One is a .480" bolt face. The other is .390". An M-16 extractor is out. It'll invade the hole the striker moves back and forth in. A Sako style could work but as far as I'm concerned those things are dangerous, are junk, and should be avoided at all costs on a 180* twin lug action. Sneeze a case and witness it whistle past your face once. You'll be of the same opinion.
Running a DBM setup will help to mitigate any brain damage from feed lip width differences.
This is easy to do, but you will have more work involved than you may have initially considered.
Good luck
C.