My T\C kit gun, that I acquired in the late '70's was and still is used for hunting. I believe my factory barrel was made not only on a Friday, but with the last pull-thru broach before it was replaced.
The barrel just never grouped well no matter ball\patch\lube combo that was used. And I had a lot of years in "try this 'n try that."
I bought a drop in GM barrel for it and it was....for accuracy and velocity.....the best thing I did for that rifle.
Now that GM no longer makes the "drop in" (a misnomer as my flash hole is a bit offset from center of the pan) if you're looking for better accuracy, and deeper cut barrel groves, I'd go to the rebore route. If your current setup works well, then just leave it alone.
My Leman build has a GM barrel in .54 cal, so going to a rebore and "thinning" the walls is no big deal. My Leman has a 15\16 wide barrel and I shoot 110gr FF all day long with no issues.
Of course, you could always buy a GM (or other) barrel to replace your existing barrel. Then in the future, put the factory barrel back on and build another rifle with the GM barrel.
You have options from do NADA, to doing something. The T\C is not a period correct front stuffer, but it is a firearm that allows an owner to extend their hunting season depending upon State laws, and allows the owner to "bang it about" in the woods without too much concern of dropping value. And it gets the job done. (A useful tool just as the original front stuffers back in the mid-1800's were)
All that can't be bad for a gun valued at $300 more or less.
MHO