Plan of attack for DIY chimney sweep

[SammyGeeks]

This is my first year seriously heating with our Progress Hybrid. The stove has been great, but at this point I'm sure the chimney needs a sweep. I don't think I'm up for doing it from up on the roof, so I'm trying to figure out if and how I can attack this from inside. There's no access to the flue from within the Progress, so I'm wondering if I can take out a section of stovepipe to do the cleaning.

It looks like there's some kind of cementing where the pipe attaches directly to the Progress, but not at any of the other joints. Is that normal? If I disconnect the pipe there, I guess I'd have to clean it up and re-apply, but I don't know what product to apply. I also have a short section of single-wall before it transitions to double-wall, and I'm not sure if that would be a better place to take things apart and access the inside. Attached pic shows both locations.

This is all really new to me, so I'm also not sure if everything is supported at the ceiling/roof or if the stove is supporting the pipe and it will come down on me if I start to take it apart. Pic includes both sides of where it goes through the roof (outside pic is actually from the other stove that we don't use, but it's the same set up for both).

Any advice appreciated