How do people get in there?
People are usually too large to fit. What you need to do is become acquainted with some of the more modern cleaning solvents instead. The chemistry keeps advancing, and the best ones available are different from what they were just ten or fifteen years ago, and with proper use, will eliminate the need for a brush.
Begin by reading
this article. It is already seven years old, and already too old to include some more recent developments, or some were so new at the time that the author probably missed them, so I'll get to those below.
The most important thing I can think of is to make you aware that carbon hardens with age. Even an hour makes a difference. The older it gets the harder it gets up to a point. As another board member pointed out, if you decap primers at the bench immediately after shooting, the carbon falls out. By the time you get them home, a lot stays behind. So, you really want to get some kind of carbon softening solvent in your bore at the range, before you pack the gun up.
These days, at the end of a shooting session and while the barrel is still a little warm, I pump spray a squirt or two of Boretech Eliminator into the breech end of the chamber and plug both ends and let take it home like that. By the time I get home, a patch wet with more Eliminator pretty much takes it out. A couple of such patches with five minutes inbetween for the stuff to work usually has the bore done.
The other product I take with me is a pump sprayer of Gunzilla CLP. That stuff is an excellent slow carbon solvent. I spray the bolt with it and let it work on the drive home, too. The main nuisance is protecting the gun case, and chamber plug and Neoprene muzzle stopper and a plastic grocery bag for the bolt have to come with. The bolt wipes clean when I get home.
Most carbon removers work by penetrating and getting between the carbon and metal. The surfactant ones actually help suspend the carbon. They work well, particularly KG Industrial's KG1 Carbon Remover and Boretech C4 Carbon Remover, and Boretech Eliminator has some of the carbon removing properties of C4, but is not as strong. Eliminator is general purpose in that it combines some carbon remover with copper solvent. Both KG1 and C4 are indefinitely reusable, where Eliminator's copper solvent gets consumed. But only a couple of products actually seem to actually break carbon bonds down. One is the the Slip2000 product mentioned in the article. Another is the Gunzilla CLP. Both can turn hard carbon into sludge with enough time to act.
The Slip2000 is the faster acting product. However, it can't be left too long on metal or it dries to a film that attracts moisture and can cause rust, as the instructions warn. It also slowly etches Parkerizing (guess how I know), so I use it mainly as a last resort and for extremely thick deposits on stainless steel, such as inside an M14 gas piston.
Gunzilla is funny stuff. It's a vegetable based solvent/oil. The main thing about this stuff that I like is that it keeps working on carbon, albeit slowly, and can be left indefinitely as it actually leaves a lubricating layer behind. I have had experience with a couple of examples of extremely hard, aged carbon which it has not only softened, but caused to fall off the steel. But it takes time. Overnight is a minimum for an old deposit. In one instance I had decades-old carbon glazed in a Springfield '03 barrel's pits. It was so impacted and burnished that it actually looked like an extension of the bore surface (except darker color). That required allowing the stuff to sit weeks, but in the end it all fell out along with rust in the bottoms of the pits, leaving the pits clean.
Copper solvent action is very good with Eliminator, but if you have need of something even more aggressive, KG12 has that and the most copper capacity. Wet patch a bore with it and fifteen minutes later the copper is likely to be gone. The only downside is KG12 turns orange brown as it acts, and not blue or some other color that makes the absence of copper easier to detect. So you may want to finish with Eliminator to see that the bore really is clean. Just be aware that Eliminator acts so fast it will be blue from the brass your jag is made from faster than you can push it through the bore. You need to use plastic jags or Boretech's special alloy Proof Positive line of jags to avoid the reaction.
The only thing not addressed well by the above products is lead. For that I use Wipe-Out's product called
No-lead. You patch it in and leave it for an hour. When you come back the lead has been turned into some kind of crusty black material that patches out.
So, here's what I would do in your shoes. Since you have old carbon, I would get some Gunzilla CLP. I would get it in the bore and in the lug recess. If you think the carbon has been there for months, let it sit a week, patch out, repeat if necessary.
For your receiver lugs, Sinclair makes a
lug recess cleaning tool for the AR receiver lugs that uses medical cotton sticks sort like the ones the dentist packs your mouth with and puts them through an eyelet so you can swab the lugs with them. This can be used in other bolt guns if you move it around and bias the cotton swab to the side. That swab can apply Gunzilla and wipe it off later. Once carbon has been softened, though, a blast with a solvent like Bore Scrubber will also remove the Gunzilla and the carbon with it.
Once you have the carbon out, you want to look at removing copper or lead deposits, depending what kind of bullets you've been shooting. If copper deposits are heavy, you may want to use KG12. I would remove all traces of Gunzilla first, as it's hydrocarbon, so a squirt of Bore Scrubber or carburetor cleaner (Autozone Carb+Choke Cleaner P/N A7000 is sometimes on sale and is the same as Berryman B12 but at a lower price, as near as I can tell). Either will remove hydrocarbons so the water-based KG12 or Eliminator can work best.
Finally, you can prevent some degree of carbon formation sticking to the bore by avoiding the usual hydrocarbons based gun oil.
Slip 2000 makes a synthetic gun oil rated to 1250°F. Other synthetic oils are out there, and I've seen synthetic 2-cycle engine oil suggested, but its ignition point is lower than that, from what I can find on the web. Just be sure you're buying the highest temperature tolerance you can.