So here's an update: after much searching, I found a video that shows how to disassemble the lenses of a pre-war biogon:
I got the special rubber lens wrenches that they worked quite well once I overcame how tight some parts were screwed together. The back section eventually came off and I cleaned it a bit, but not much needed so I focused on the front. It didn't seem to budge. I resigned to use one of those caliper using tools for retaining rings on the front when the rubber things weren't seeming to cut it. Well... that slipped and thankfully only scratched a tiny bit of paint, unfortunate though because it was all otherwise unmarred before. Still, the glass didn't get hit.
So now I've sworn off the evil torture device looking thing for removing retaining rings and am back to the good ol' Japanese rubber cone thingies. Uhm, would you be mad at me if I told you it loosened the next time I tried turning it?
I found it's mainly the front element that has some annoying haze. There was some fungus floating somewhere that I couldn't seem to reach with my cloth. The haze "felt" the same, even though it lit up on the front element really bright in the light. Couldn't feel a texture difference with my fingertips. A bunch of scrubbing (lens cleaner + microfiber cloth) didn't get it off.
Either way, I reassembled it and it did in fact look clearer. Besides maybe a tiny bit of fuzz that might have been left by me. I'll need to get better at this.
Also, this might be strange, but the issue with the lens barrel does NOT seem to be an issue for using the lens. Seemingly.
I don't know if I had done it wrong before but I was able to mount it
halfway (the red dot is at 1 o'clock instead of 12). And I was worried about whether this issue with the barrel would screw things up with the focus. Then I realized: the focus helicoid is all that matters, not the distance scale. If it's pressing the coupling mechanism by something directly attached to the lens groups, it should still be "accurate", no?
First things first, the focus ring move the focus patch. So that's good.
Then, focusing on a bright light at infinity causes the lens to stop here:
Unmounted it turns a tiny bit more, so the infinity tick is over the 2.8 tick. There's still an issue with the aperture being stiff, which might be understandable because it's difficult to turn, but it's not as easy as all these other videos that I thought mine might be entire stuck.
So, despite all this strangeness, things seem like they can work. Of course I'd like to know how I can fix this issue but I'm gonna see how this fares!