I'll diverge from the others and recommend 1:11 twist. It is fast enough to stabilize everything up to and including 210grain bullets. In the end, it doesn't really matter if you go 1:11 or 1:10. Just don't go 1:12 as that will limit your bullet selection.
As for who should do the rebarrel, I would not recommend Hart in PA. Search LRH and will find many that have terrible experiences working with them. The 'other' Hart in New York is the better part of the family to work with.
Hart Rifle Barrels
The Surgeon is right about having your barrel crown checked-out. You might have unknowingly hit it on something causing a small 'defect'. Most gunsmiths will recrown your barrel for ~$50 or less.