There are 3 custom barrel manufacturers that I would consider:
1. On Target Technologies
2. SSK Industries
3. Match Grade Machine
Of those, the only one I've gotten a barrel from is SSK Industries so hopefully someone with personal experience with the others will chime in. Though I haven't used them, the other two have a very good reputation.
Counting Encore and Contender barrels either of the regular sort or from the T/C Custom Shop (a.k.a. Fox Ridge Outfitters), I've had 2 or 3 dozen barrels. In all those barrels I've had 3 problems:
1. With a Contender barrel, opening the action was very difficult probably because of no easy open modification. I returned that barrel to the seller.
2. The factory had neglected to tap the holes for the forearm on a 7mm/08 handgun barrel. I returned it and they fixed it.
3. I have a 30/06 barrel that, when I got it, would throw the first 2 or 3 shots from a clean barrel fairly widely. I returned it to the factory and they recrowned the barrel (it didn't look bad to me) and fire lapped it and it now easily does consistent sub MOA with a variety of bullets.
I know there are occasional problems with the barrels of the custom guys so considering the number of barrels I've had, I don't think the number of problems I've had is way out of line. T/C has also been excellent about fixing stuff under their lifetime warranty (a couple of scopes) at no charge even when they knew I had not bought it new.