Dimensioning RMH to existing chimney

I have a wood-burning cooking stove installed to a existing chimney in my house now. It´s an old unit and it doesn´t burn particularly well. It always smokes kind of partly black despite going full blast and it smells outside. It also produces quite a lot of creosote in the chimney pipe and even some almost grass/algea-looking ash fibers inside the unit itself. Still, it is very usable and cooks and heats well, but I have to do something about the dirty burn to partly not needing to clean the chimney every 3 months and partly to not make the neighbours cough.

This have lead to the plan to replace the cooking unit with a small batch box rocket mass heater with a directly feeded brick bell. The problem I have is to decide the dimensions, and I am not totally sure that the current chimney solution will work. I think part of the current dirty burn problem is caused by the chimney. It is a strange solution (not made by me, but from the previous owner of the house. Going from the stove and up, I have 120mm (4.7 inches) pipe from the stove. Then it goes straight up to a 90 degree turn, then left horizontally 20 inches, then turns 90 degrees again and goes horizontally straight forward into a brick chimney, then turns ANOTHER 90 degree turn upwards into a small about 6 times 6 inches rectangular chamber (seen by an inspection camera) and then exits up to a straight 3m 100mm steel pipe (3,9 inches) that is inside the old chimney. So it is basically straight up, then turn-turn-turn-chamber-pipe reduction-straight up through the roof. My guess is that the turns and the volume reduction of the chimney along the way destroys the draft possibilities and creates a tough task for the stove.

The pipe inside the chimney is not easily replaced and my guess is that they had problems fitting a 120mm pipe and then went for a slightly smaller option just to get it down.

Anyway, what would you say would be the best dimensions for the core design for the RMH? And how to do with the chimney to try to get as good draft as possible? Is it better to go 100mm to be sure that I don´t over-feed the upper 100mm pipe? And then replace all external pipes outside of the chimney to 100mm. Or do you think that a 120mm core can work with a 100mm chimney pipe? I for sure don´t want to risk back-smoking or lack of draft again, since I have that problem today already and that is what I am trying to solve in the first place.

The bell size is no problem. I can do whatever fits, basically. I have plenty of room. So it is only the burn quality and safety that matters, really.

The chimney will play a big part towards the stoves performance, every bend or elbow will effect the flow.
Your chimney sounds just about as bad as it can get!

Indeed, I agree with Fox, all of the bends and the size reduction make this a real challenge to flow!
Rocket stoves, be they J-Tubes or batch boxes need a good draft to flow.
Without a good draft, they will seek and locate an exit indoors... it is not a fun experience at all!

To attempt to use your existing chimney, I suggest staying with a 100mm pipe from the batch box through the roof.
You can only build a 4" batch box, so it will use much smaller wood (branches) but needs to be loaded more often.
Removing the 90-degree bends would help enormously, perhaps two 45-degree curves spaced apart?

Your brick chimney that has the 100mm pipe stuffed in it...
It is possible that the liner could be removed if the bricks are sound and then you would have a 150mm chimney.
You could also build a 6" batch box rather than a 4".
Exhaust temps are low enough that a burn-through of the bricks is not a concern,  leakage however is a problem. A good inspection would be needed.

While I won't guess about the possible size, I would like to suggest a simple way to check for draft long before the stove be built.  At the base ( where you would hook in, you should be able to take a wad of single sheet of news paper,  and have right at the opening ( not on your fingers)   and when lit, the heat/draft should be noticeable and with a box of 10 or so single sheets wadded up, feed each one as the other burns.  This should soon be almost sucking out or your hand the next sheet of paper.

This paper burns fairly hot for a brief bit, thus inducing draft with the rising heat.  If your fearing your chimney is already coated with creosote, be careful This process has  been used to carefully  burn out a chimney, but you  have to be able to stop the inflowing air if need to do so.

I would think you would want to know if you have a fairly decent draft in place before any further decisions.

Best of success.  (by the way, if you have decent draft, this test should produce NO smoke in your house, if you don't have good draft, your smoke will be limited to one sheet of paper, a small price to pay, vs a wood stove burning with no where to go)