I've never had a No. 1 rebarreled, but I would go with Mark Penrod. I used him for another rebarrel on a custom Mauser in 7mm Rem Mag had he does excellent work and he also has a good reputation with No. 1s.
I had a #1 re-barreled to 300 H&H (28" Krieger) by Ed LaPour. He spent some time telling me why he thought the Ruger factory set-up with their 1/4 rib and hanger put un-even stresses on the barrel. I can't remember the details, but the rifle he built (including a new trigger & safety) and that Al Lind subsequently stocked is still one of the most accurate and non finicky rifles I own.
Curious about the "hanger" on the No.1 and 3 rifles for they are not attached to the barrel are they or at least mine are not. Hanger is welded to the lower part of the action itself and forearm attaches to that with angled fastener avoiding any stress on the barrel it would seem?? I had Douglas retired fellow do two re barrel jobs for me and in fact the No.1 has two barrels/switch barrels if you will, one in 22-250 and other in 348Win. Change of extractor required due to rim/case diameter, but not at all hard to switch and extractor itself is very reasonable in cost. No.3 done with heavier/longer barrel than factory for 45/70 Gov't. Very easy to handle and with the Ruger action you can load that 45/70 to a level beyond most people's tolerance for pain, not a bench gun. The No 1 w/ 22-250 26", 7 twist barrel, and Unertl 16x scope and 80gr. bullets is an excellent long range combo easily giving sub MOA groups of 5 at 100yds. For varmints of say coyote size the 69gr SMK would work fine and equally as accurate out to some 500yds. plus, but not for extended ranges as in 1000yds. If you go to Ruger's web site you will find videos for the disassembly and re assembly of either action(other than lever system are the same) and take one apart and you will appreciate the engineering and robustness of the action even more. In the early days of these projects thought I could find me a factory barrel an fit it to the action, wrong thing to try for the face of the actions will vary ever so much, but barrel must be fitted accordingly per action. No big deal with Douglas being some 10 or 12 miles from home. Used the factory rib on the 348 and with NECG peep sight sitting on that with NECG barrel band front sight and bold brass blade it is easy to shoot off hand for it offers very clear sight picture and balance is near perfect for me. Great rifles those Ruger No.1's and 3's. Now if I could only come up with sufficient "scratch" would send both off to Turnbull and have the actions color case hardened and follow up with a trip to Wenigs for some 4x walnut stocks. No harm in dreaming.
I've mostly been pretty happy with my own re-barrelling/building efforts and, when I was not, I gave myself a stern rebuke or two and things were quickly rectified. I like the Ruger No. 1. Number Ones are a little more work than a typical bolt action but are an opportunity to pretend to be a real gunsmith and pretending is all I've got. Regards, Bill