I sympathize with you PA. I can tell you from experience that TC's can be a total PITA trying to get them to shoot. I have an Encore that has had 3 factory 22-250 barrels replaced without any luck. I finally just rechambered the last barrel to 22-243 Midd and still worked my tail off getting it to shoot below 2". Barnes 53 TSX's went 3", nice triangle but wouldnt get below 2". I shot up a full box without any success. First 3" horizontals, then 3" verticals, then back to 3" triangles. The original bug holer loads were 36 to 39 gr H4895 and a 53 gr Hornady match HP. They ran in the 1 - 3 thou range with the original Rem 40X 1 - 12 twist barrel.
I've been doing T/C's for near 30 years and this I can tell you...factory barrels...either they shoot or the don't and to get the poor ones to shoot is tough work. After market barrels are another story.
The problem is the reciver/barrel is flexible, you are shooting off the forend that is attached to the barre or grabbing it hard for a hunting shot, and that can impart strange vibrations if you don't use correct sandbag shooting proceedures,(or learn what hold works best in the field) and the forend usually contacts the receiver someplace and again causes problems. The T/C barrel is none to stiff even with the bull barrels.
My 22-243 has gaps around the receiver you can throw a cat through and I milled dovetails into the barrel, a la Contender, installed 5/8" studs held by set screws, then installed a 3/4" x 1" aluminum bar into the forend milled and drilled to fit the barrel studs. The forend is solid being torqued to 120 in lbs, doesn't touch the receiver and I finally hit a combination of H4895, Sierra 53 gr HP #1400, a 2.575" OAL - just touching the lands, WW cases and Fed 210 Match primers. It still isn't a bug holer but it is hitting 0.650" most of the time, and still below 3/4", but it won't shoot the 53 gr Hornady's. I will live with that until the barrel is gone.
I will never have another T/C anything and will get rid of the ones I have over time. Break action rifles have inherent problems that are hard to overcome and continue to complicate the picture until you give up, sell out or use it for a jack handle.
That being said, if you can live with "hunting" accuracy, 1 1/2" plus or minus 1/2", T/C's are excellent, there are lots of ways to attach the forend and a few places to obtain aftermarket wood if you want to play DIY. T/C's are things of beauty and a joy to behold.
My first and most fervent advice is to send the whole package to someone who deals with accurizing T/C's, like Mike Bellm,
http://www.bellmtcs.com/, who did one for me way back in the day and I trust. At least he doesn't rip you off and will examine your rifle at a nominal cost and tell you what needs to be done, then do the job, again at a nominal price. You will be miles ahead unless you are into S&M, like pain and want to do it yourself. If so, then start searching the forums and 'net, all the pertinant information is available.
Things to do and first things to check.
Check the head space. Go to Bellms site, he has the best explanation I've found for T/C's.
Get a new bolt, measure and order a hinge pin and lighter trigger spring from Belum. (A Matter of course in Mikes evaluations) All mine have 1 1/2 lb trigger springs.
Check the throat depth. My suggestion is purchase a set of Stoney gages. Measure and record the numbers. Depending on the caliber I start at 0.020" off the lands for 22, 6mm, 25 cal's, 0.010" from 26 to 28 cal, and 0.005" to just touching for anything over. Just places to start and not set in stone. My 338-06 has a throat soo long nothing touches, so I seat to fit the Rem 700 mag and the bullet. The Hornady 225 gr and Nosler 200 gr shoots 5 shots you can cover with a quarter at way over book numbers because of the "freebore", but it won't shoot any other bullets into anything less than 1 1/2" for 3.
You can have any machinist check the runout on the chamber and to see if it is straight or not. T/C's are known for bad chambers!!!
Then, after that is done, and you want to continue the process, I would glass bed the forend from stem to stern. This has helped many a "bad" barrel. If that doesn't help you can just put a small washer on each screw and make the barrel free floating. But you MUST make sure the forend doesn't touch the receiver ANYWHERE, including the hinge pin or you will get patterns instead of groups.
These and many other things I do/did to all my T/C's to get them to shoot, just about in that order. I was successful in 98% of the time.
Good luck!!!??