Remington has a Rem Oil Bore cleaner containing a jeweler's rouge-type compound to remove stubborn fouling, but Bore Bright is a Brownells product, a very fine polish, to use at the end of a complete cleaning of chambers and bores.
Brownells J-B Bore Cleaner, paired with Kroil, is an excellent bore cleaner. It saves a lot of needless, tedious scrubbing of the bore with solvent patches. Use it after an initial brushing with any good solvent and patches. Hoppe's or Ballistol is fine. Then clean with the J-B and Kroil, allowing the Kroil time to penetrate. Wipe clean with patches wet with Kroil. Any slight residual fouling can easily be removed with more J-B/Kroil or a specific copper or lead remover.
In a pinch, a touch of Simichrome polish or Flitz can be used on a patch wet with solvent to clean a bore. Just don't over do it, and thoroughly wipe and/or flush the bore clean afterwards. I am recommending no more than 6 or 8 passes to break up fouling. Finish cleaning with a good solvent. Butch's, Sweet's and Montana all seem to have their proponents fir removing copper fouling; just follow instructions to the letter.
You do clean your rod, wiping it between each pass down the bore, always use a bore guide or muzzle guard, and always wash these, your brushes, jags, etc. in warm water and detergent, and drying them after each cleaning session?Why of course!
It is interesting to read where people will clean their chambers and bores with Hoppe's and re-clean the next day with another agent. When they find more residue on the patches, they immediately declare Hoppe's to be inferior, inadequate for the job.
What they should do is try the reverse after another shooting session, keeping the conditions the same. Clean first with the supposedly "superior" product, wait a day,then reclean with Hoppe's. The residue will almost always appear again. That's because the truth of the matter.is that each solvent has different strengths snd weaknesses. No one solvent does it all. My own practice is to clean with either of any two solvents, removing traces of the first with naphtha on patches before employing the second solvent, or by employing J-B Bore Cleaner/Kroil or the similar but not quite as good (no Kroil!) Remington Bore Cleaner.
We don't have to be fanatical at each and every cleaning. But it nice to know how to render an arm very clean.
Hoppe's with T3 is a very good lubricant, excellent on actions and Hoppe's "Black Rifle" line certainly deserves investigation. My experience with the carbon remover has been very positive on an AR15 BCG.
The lubricants recommended by Grant Cunningham in his article on gun lubication (Google it) continue to be improved, and they were a pretty darn good oil and grease to begin with. A solvent has now been added. Just buy the package and stop fretting.
Nyoil is recommended by Grant, and if you use it, you will see why. It is safe, clean, general purpose gun oil. It should be much more widely used, as it is both economical and effective. I will be putting some of it up in a little to-go bottle for range and field. Anyone sho uses or would like to use ATF as a lube or cleaner, should use Nyoil instead.
Brownells Action Magic should see wider use in protected areas on actions and triggers (it is grey/black due to moly-D content), where it will protect metal from corrosion as well.
The Tetragun line has continued to impress me, especially their grease, beyond my expectations, for three decades now. If I give a cleaning kit to a new gun owner, I now always give the Tetra Gun lubricant psckage as well. It has fixed some issues in guns that had more than one good gunsmith puzzled.
Superlube -I am not sure, but I may give it a try. i speak here of the grease and thick oil formulations WITHOUT silicone!
I am very involved with lubricants as I refurbish okld (but very fine) microscopes, and the mechanisms are exquisitely sensitive to the the properties of lubricants used. There is one rack lubricant I have to use, which gives the right touch for focussing, which costs $50 an ounce. Others are less costly, but still specific. For instance, in an enclosed space with optics, the lubes cannot offgas. Otherwise deposits will form on the carefully cleaned lenses.
Then there are the lubricants which have hardened over 40 years. They must be chipped away.
So by contradrt, firearms are fairly forgiving. And modern lubes are, by and large, a great improvement.