This is more of an all around cleaning post, in response to the carbon ring question. For getting rid of the carbon ring, I have used many methods, but I recently watched a video from the Bolt Action Reloading Channel on YouTube and I would agree that his method is one of the best, fastest and easiest I have tried. Use a Nylon brush at least 1 caliber bigger than the bore (for 308 caliber, use 338; for 7mm (284) use a 308 brush, for 6.5, use a 7mm, etc.). Put the brush on a chamber cleaning rod or your full length cleaning rod if you don't have a chamber rod, Center a big patch (2.5-4 inch size) over the brush and soak the patch with a good carbon remover such as Boretech Carbon cleaner or KG 1 Carbon cleaner. Insert the wet patch/brush in the throat/chamber (your bore guide should be removed) until it stops against the rifling, spin it a few times and leave it set for 12-15 min. After it has set for this 12-15 minutes, Spin it a few times and this will usually remove most of the carbon. I flip the patch over and use the clean side and spin it again, a few more times. Using this method has taken almost all the carbon ring out quickly and without a lot of scrubbing and hassles I used to use with Nylon and Bronze Brushes. Silencers tend to increase the speed that a carbon ring can form also. Before I clean the chamber as stated above,, i have already run a wet patch with a solvent down the barrel and then stroked it with a brush 15 plus times.
While the barrel is soaking in the solvent, I remove the bore guide, then I perform the carbon ring/chamber cleaning process I listed above. After removing the carbon ring from the throat, I finish cleaning the barrel with solvents Like Boretech Eliminator, KG 12 Copper and KG 1 Carbon Remover, Butches bore shine, Wipe out/patch out with accelerator, Shooter Choice, etc. I have good luck with all of these, but prefer Boretech for now. For a more abused and/or dirty barrel and/or every 100-200 rounds, I use Thorro cleaner/Flush (there are 2 bottles in the pack and I got them from Bullet Central), Witches Brew from Holland guns, Isso bore paste or JB paste with Kroil and/or a light solvent, etc.. If you don't use an abrasive or strong solvent, I have found a bronze brush is necessary to remove carbon and copper unless you like scrubbing your barrel a long time with a Nylon Brush. Keep in mind that the bronze brush will give you a false positive on copper when using a copper solvent. I have never damaged a barrel with a Bronze brush, but I am sure all things are possible. I use Boretech, Dewey or Tipton 1 piece rods and Boretech or Tipton jags with the sharp point on the end or a TCS jags with the rubber O-rings. I have many different type and sizes of patches, but the square ones are more universal, as you can poke the patch near a corner if you want a loose fit and in the middle for a tight fit. The third option is to use a smaller than caliber nylon brush wrapped with a 1 3/4 inch patch. Nylon brushes work better when used with one of the more abrasive cleaners I listed above as I find them a bit slow for me compared to Bronze bronze and standard cleaners. When using a copper cleaner, always finish the cleaning with a nylon brush so you can tell if the Blue/green color on the patch is from the bronze brush or actual copper in the barrel. I short stroke (3-4 inch back and forth) the brush/jag with the abrasive cleaners until I reach the end of the barrel, and then use the Nylon brush (15 to 20 strokes) between the wet patches. I wipe the rod down with a shop towel after each cleaning series. Repeat as necessary until you get the barrel pretty clean or really clean, depending on your goal.
Use a bore scope to check the carbon ring and copper/carbon in the barrel to verify the level of clean you have achieved. Try different methods to find what works best as there is no 1 cut and dried way, but there are many ways which are not good also. Generally I don't mix solvents from different companies without running a dry patch through the barrel first and then switching. After the barrel is cleaned, use Q-tips or similar swabs to clean muzzle break holes and the muzzle brake chamber, Use a Chamber/bore mop or a larger nylon brush (like 375, 416 or 458) with a shotgun patch on it to clean the chamber of any solvent residue and then use one clean patch on a jag to push any solvent you pushed into the barrel from the end or the chamber. If you will store you gun, you can run 1 patch with oil or bore conditioner down the barrel and then follow with 2-3 dry patches. Do one last stroke in the chamber with the chamber swab to remove any of this oil. Most of my shooting is with magnum or 6.5mm and larger calibers or faster varmint calibers. Normally I hunt with Copper type bullets: Badlands, Cutting Edge, Barnes, etc. which will foul a barrel faster than a Berger, Sierra Match, Nosler ABLR or a Hornady Eld-M or Eld-X so I usually clean after any wet hunt (to prevent rust) or after 20-30 rounds at the range when using Copper bullets. Two of my old Pre-64 rifles need their barrels cleaned after 12-15 rounds with copper bullets or I will start to see accuracy issues. These older barrels still shoot well, but they will foul a lot faster than a High end/custom Benchmark, Proof, K&P, Krieger, Bartlein, Brux, etc. Target and varmint bullets don't require as much cleaning, but each rifle is different. I almost never shoot my 22-250 or 6mm CM more than 50-100 rounds without cleaning them, even though I could shoot more. I just never found any of my barrels to shoot better Dirty than reasonably clean. Generally I only need 1 or 2 rounds to get the barrel "fouled" after cleaning the way I do and I always check each rifle to see where the first round goes from a perfectly clean barrel. Each barrel is different. I know that many PRS shooters will go 200-300 rounds between cleanings, but they are shooting less powder and lower velocities than a 22-250, 7mm, 300 Mag, 338 Norma, 6.5 PRC, etc. especially when using lighter weight and faster copper bullets.
A couple other tricks: Always use one of Green Plastic Patch catchers from MTM on your barrel to avoid, drips, wall/floor splatters. I also add solvent at the barrel (inside the patch catch) to my brush every 5-10 strokes, so any extra solvent doesn't get on the stock or drip on the floor. Adding a bit of solvent every few strokes works better than saturating a brush and having it drip on the stock or action. Some bore guides have a slot to add solvent and some don't, so you can add solvent there too. After using an abrasive cleaner or a really strong solvent like Barnes CR10 or Sweets 7.62, always runs a few dry patches, then do a cleaning series with a milder, non corrosive solvent like Boretech Eliminator or even Hoppes 9 to get all abrasive cleaner and strong solvent out. Some people even use Isopropyl alcohol in their barrel, followed by Bore Conditioner/oil as their last cleaning step when using these copper solvents, but I don't use these super strong copper solvents on my Stainless barrels anymore as I heard they can etch the barrel. Also, CLR which is sometimes used for Carbon removal can etch steel if left for too long. Use Isopropyl or denatured Alcohol to clean off the nylon and bronze brushes after you are done, as they will last longer and it will remove any carbon and old solvent from them. I put my solvents and alcohol in 2 and 4 oz squeeze bottles with steel tip applicators, which I got from Amazon so I don't waste or spill solvent.
I hope this long detailed cleaning post is useful. Good shooting.