Have your barrel maker stress relieve the steel first. Yes, I know the steel maker says it is stress relieved from his shop. Don't believe it. Drill the barrel, stress relieve the barrel again. Then flute the barrel turning it 180 degrees, between passes. Now stress releive the barrel again. Lapp the bore, and button or cut the rifling. Turn the contour and stress relieve again. All the better button barrels are stress relieved at least 3 times. The process is different with cut rifling.
Thre are three methods of stress relieving, heating in a heat treating oven, vibratory bead method, and cryogenic. Not being an engineer I can't say which is best or if a mix or match combination is better. I can tell you the top barrel makers will all agree that stress and heat are the bigest enemies to a barrel and accuracy.
I highly reccomend talking to the barrel makers themselves. They will not let out their propriatary trade secrets, but they will give you the basics.