Mine is a Sako TRG-S. It does have a muzzle brake. The muzzle brake is a KDF clone and works VERY well (I have 3 other rifles with various kinds of brakes and this one works the best). The rifle can be shot one handed, benchrest style from the bench, the biggest drawback is the gun is VERY loud. You are in the same boat as my brother, being left handed, but he also bought the TRG-S.
Who are you thinking of for the barrel work? Currently, I am having Pac-Nor build me 338-284, I have a Krieger built 338 Win Mag, a Blakcstar 7 STW, my Dakota 76 has a Lothar Walther, and they are all great. I have used Lilja, Hart, and Shilen before and they are all first rate. I think Pac-Nor is the least expensive, they charge $220 for their best grade barrel and $200 to chamber, thread, install, lap lugs, and true the action. Their turn around time should be 8-10 weeks. If you're interested, I'll let you know the results of the 338-284 as their 338 barrels should be pretty much the same.
Jim