Tar Buildup in Chamber

First post. Have tried in vain to find some help on this through searches, but it seems rare that people get tar build up in their chambers (referred to as sludge cake, I believe), so I thought I would start a new thread on it.
I have a relatively new Bjarne Viking bent apple that came with a carbonized chamber coating. Have probably smoked on the order of 20 or more bowls with it, starting with half bowls for the first 4-5 smokes. Mostly smoked Dunhill 965 and Nightcap in it.
About 5-6 bowls back, the tar buildup first showed up, and there was bits of tobacco from the last smoke embedded in it. It took some significant scraping with a pipe tool to get the tobacco bits out of the pipe. No amount of scraping would get all the tar out though. Tried smoking it again thinking maybe another bowl would harden the tar, but it didn't, and the smoke tasted horrible whenever the ember would burn up against side of the chamber.
At this point, I did the cotton ball and alcohol treatment to the chamber. That removed the tar, but the cake that was left on the side of the chamber walls was soft and powdery, and it was relatively easy to flake/rub off the carbon buildup. Smoked another bowl and that left enough tar in the chamber to hold the carbon in place. However, the last 3 smokes have resulted in enough sticky tar buildup that I need to use alcohol to clean the chamber again.
I think I am drying the tobacco enough, as it doesn't stick together before packing, I don't get gurgle, what dottle is left over appears dry and charred, and there is no moisture visible in the bottom of the chamber.
I have used multiple packing techniques, 3-step, Frank, air-pocket. It might be possible that the latter two methods create more tar than the 3-step method, but I can't say for sure.
I do use a pipe cleaner after every smoke to clean the draught hole, mortise and stem, and it doesn't appear the tar buildup in these areas is all that bad compared to the chamber. Once the pipe cools down, I also ream out the inside of the chamber with a folded up paper towel. I generally don't smoke this pipe more than once every 2-3 days, so it has plenty of time to dry out in-between smokes.
I don't have this problem with my other two pipes (yeah I am just getting started), one reserved for Va/VaPers and the other for Cavendish blends.
I am still learning on ember maintenance, and it is common that either I need to relight often or the ember burns down the center of the tobacco pack. I do need to do better on the evenness of my false light, using my tamper more often and keeping the ember wide and thin (that last part I would be happy to get tips on, but don't want to derail from the original subject).
Lastly, I should note that I smoke outside, and humidity is usually in the 70-80% range, so I don't know if that has an effect or not.
I am contemplating taking some steel wool to the chamber after the pipe dries out from the alcohol soak and removing everything down to the wood and starting over. Thoughts on this?

Thanks for the reply Sablebrush. I do use a paper towel to clean out the chamber as you describe above, although I usually do it after the pipe cools down. At that point, the tar is too sticky and thick to get off with a paper towel. At best, it just causes some of the tar to ball up, but there is still plenty more left behind on the walls. I will try cleaning with the paper towel while the bowl is still hot and see if that works any better.

With a little more testing, it seems that my problem probably most stems from smoking 965 in this pipe. Smoked a bowl of this a couple days ago, and while the cake had not been gummy beforehand, was after. Also, the smoke was pretty harsh compared to all the other blends I have smoked in the pipe, so it seems to be the main culprit. The tin had 2 years of age on it before I opened it FWIW.
Just smoked a delightful bowl of London Mixture in it tonight, with the bowl still gummy, and the didn't have any of the problems with the smoke being harsh when the ember was up against the side. Afterwards, I gave it a pretty good cleaning while the briar was still warm, by scraping out what cake I could with my pipe tool. and then followed up with a paper towel. That left a thin, slightly sticky coating on the bowl, with the wood slightly visible in some of the scratches left behind by the pipe tool. Rubbed in some leftover ash from my smoke, and things feel and look good at this point.
The bowl coating could also be the issue, although it looks like it has mostly been "dissolved" at this point from what I can tell. I do remember after the first couple of smokes in the pipe, that the coating seemed to be peeling off in places on the inside of the bowl, so it must of had some sort of polymer mixed in with it.
It does appear that some varnish made it into the chamber on the very upper edge, but it doesn't appear that the chamber was varnished below this.

A follow up on how things are going and some further thoughts on the issue. I have had this problem in other pipes now as well, although not quite as severe as originally with this pipe. I think I was still smoking the tobacco too wet, and I wasn't letting my pipes dry out enough in-between smokes, even though I was waiting anywhere from 2 to 6 days between smokes in this pipe.
Basically, the problem seems to stem to the fact that I keep my pipes and tobacco in my basement, and the humidity in my basement seems to be fairly high. When people say they let their tobacco air out for 10 minutes to a couple hours, I can only assume they are dealing with much lower humidity. This became apparent when I started smoking my pipe while I was out of town, finding that the tobacco dried out much more quickly. Basically to put things in perspective, if I were to take some ribbon cut tobacco directly out of a fresh tin of say some Dunhill blend, I would have to let it sit out for about 4-5 hours for it to reach the proper moisture for smoking. With flakes things are even worse, generally 3 days for an intact flake of say Escudo or PS LNF, and even then things are still a bit on the wet side. If I rub the flake out, it has to dry overnight at a minimum, maybe even up to a day to get the tobacco dry enough. As another point of reference, I left some MC blackwoods broken flake to sit out for three days, and it was still too wet to smoke even then.
Needless to say, my pipes have a hard time drying out as well. If I left them to sit for at least 7 days between smokes, I might be okay though. I have resorted to keeping my pipes in a somewhat air tight plastic tube with a quart size can of desiccant. Doing this, it appears that the pipes will be ready to smoke again in one to two days. I still think the carbon coating on the Bjarne pipe was part of the problem, and might have been partially responsible for the harsh smokes, as the compound that was holding the carbon to the bowl broke down under the heat. That would explain why the carbon was so soft and powdery the first time I used alcohol. The alcohol dissolved the bonding agent in the coating leaving soft unbounded carbon behind.
Lastly, upon further research, it seems a little bit of stickiness in the chamber is not uncommon, and is not a problem if you keep it under control.
I am thinking I need to get a heat lamp for drying tobacco, and if I really want to get carried away, add a low-watt incandescent light bulb to the tub to keep the air circulating while my pipes are in there so that the desiccant can do its work more efficiently. That or just leave the tub close to the heat lamp.
Thanks once again for all the replies, I do appreciate them.