A few years ago I put together a .270 Win. on a Columbian Mauser action using one of the much-maligned Adams & Bennett (reputed to be E.R. Shaw seconds)barrels. I found that this rifle would shoot groups of about 1 MOA or a bit under, but only after it had at least a dozen fouling shots down the bore following a thorough cleaning. Also, it showed a lot of jacket-metal fouling near the muzzle (the only part of the bore I could really inspect without a borescope).
I gave it the Tubbs treatment with the pre-coated abrasive, using a reduced load that should have given about 1200 fps (didn't chronograph it), and the results were as follows:
The grouping was no better than the best of the pre-treatment groups, but was now much more consistent and didn't require any fouling shots to perform well.
The metal fouling appeared to be unchanged from before, as far as I could tell, being able to eyeball only near the muzzle.
My theory of what happened is this: Originally there were some rough spots near the origin of the rifling which were gouging metal from bullet jackets as they passed. After some rounds went down the tube, jacket metal accumulation smoothed out the roughness enough to allow better grouping. The Tubb treatment knocked down those rough spots, and the good grouping then became usual. I don't believe that the honing effect lests long enough to smooth out any roughness near the muzzle, however, though that seems to be not much of a problem.
In your situation, I think I would wait until I had seen what the combination would do before using the Tubb treatment. Only if there were fouling related problems such as mentioned above would I go that route.