I've loaded Barnes since about 1992, starting with the X, then XLC (blue coated), TSX and TTSX, in multiple calibers and multiple rifles.
The X and XLC were very sensitive to seating depth, and those I started deep.
For the TSX and TTSX, I start with the published COL and have not had to change COL to get excellent accuracy. A friend has two Hart customs, one in 243 the other in 300Win. With those rifles, we did adjust seating depth, but did not see any improvement so we're back to published COL.
One thing I did find, and DirtyDog already mentioned it, is the TSX and TTSX like to be pushed fast. I start at the highest powder charge and work back maybe 2 grs from Max.