My experiences have been pretty much like BCB's; some T/C's shoot cast well, others are completely horrible.
All are good jacketed bullet shooters, so if it shoots the jacketed bullet there is no reason to assume it will be competent with cast. "Poor shooters" in my definition can't do better than around 1.5 inches at 50. Frankly, for what I do, even that's marginal. A lot of my Contender barrels are in small game calibers, so what is passable for deer hunting under 200 yards doesn't meet my criteria for acceptable accuracy.
My suggestion would be to avoid T/C Custom shop barrels as lead bullet shooters unless T/C can provide detailed information about barrel and chamber dimensions in your selected caliber beforehand. Even then, I'd be leery.
I'd just like to re-emphasize that you don't necessarily have to give up on a barrel, but if the good folks here cannot help you, then consider either modifying the barrel (with no guarantee of good results) or simply relegate it to jacketed bullets only. If your T/C experience turns out like mine you WILL run into barrels that will not shoot lead no matter what you try.
Having a barrel that won't shoot lead absolutely galls me, though, so some of my Contender non-shooters got rechambered to other calibers, cleaning up the chamber and throat dimensions to the point where they now work fine. My 25-20, for example, is now a 25-35. However, after that's done, you'll have enough money invested in the barrel that you should have purchased another brand of aftermarket barrel (instead of the T/C) in the first place.
I have also heard that T/C doesn't stress relieve the barrels after welding on the lugs, or does it in such a way that the barrels are stressed. My .25-20 groups, cast or jacketed, would go completely wild whenever the barrel got even a little past lukewarm. My .25-20 and .22 K-Hornet T/C barrels (among others) are the biggest turkeys for lead I've ever encountered, but the K shoots select jacketed loads so well I've left it alone.
My 7-30 Waters barrel is pretty good with cast, though, and my .35 Remington barrel shoots lead just as well as jacketed. I hope you've got one like these, and a little load refinement improves things for you.