Re: Who did you use, why did you use them, and were you happy?
Don't forget 308nate at SSG. He did a rebarrel on a Sako TRG-S for me. Broughton #4 SS 28" in 300RUM. Bolt and barrel fluting, V-port muzzle brake, bedding job, and bead blasted finish. His work is second to none, in my opinion. Do realize that the builders you hear from, and of, in this forum, are in steady demand. So don't expect your build to be a fast turnaround. You don't want your build rushed. So you can't expect them to rush the ones ahead of you. Sounds like you have a pretty good parts list going. You might want to start ordering your parts now, if you haven't already. The Manufacturers usually have a pretty good backlog also.
There are a few BAT actions for sale on the Benchrest Central classifieds now. You might want to check there. Good Luck with your project. It sounds like a good one.