I have 4 different barrels, one G2 frame. My dad has 3 "old style" frames and "umpteen" barrels. I never (nor does he) give any thought to hinge pin orientation, sight adjustments, "winter" vs "summer" loads, etc. We even borrow barrels from each other and never give it much thought as to which frame the barrel was on originally. Generally, all of the barrel and frame combo's are capable of MOA accuracy, assuming that some homework has been done at the reloading bench. My 14" 30-30 barrel isn't picky at all, just cram whatever into the chamber and shoot.
The TC system works well for me, usually capable of better accuracy than I am. Maybe if I were big into competition, I would keep one barrel and frame together, maybe even do some tuning on that one setup. But for the most part, it's sounds like too much trouble for a very minor gain in accuracy.
I'm with Ladobe, "consistency" is the most important. From the loading bench to the sandbag, to the woods.