Hi again,

You must have a strange problem,
I still think its a fuel problem /
Or a combination of small problems.

For example the engine could be to rich on fuel at low throttle due to the "switch"/"switch chamber"(im not sure this is the name in english to say it) in bad condition in carb as these go up and down each throttle turn, then will enlarge and let to much fuel go into cylinder; check appearence.
Or/
You have dirt in the small interiour idle passage of carb; take carb off, disassemble, and blow with compressed air.
Or/
Dirt in the little breather pipe to fuel pump, it will only work with much vacum; take off and blow with air in the pipe.
Or/
Why not dirt in fuel swithes at fuel tank, then fuel will only arrive when engine runs fast, I doubt; screw off clean and oil.
Or/
Rust from tank in fuel pump membrane, I had that on mine; open pump clean with fuel.

In my mind it must be either carb or pump.
Though it could be compression of cylinder, if low it could be thhe cylinder that need a rebore or just valves who needs tto be remade; less expensive.
If you want to have an idea if the valves have the right play, take a big screwdriver with plastic hold part, run engine, put screwdriver in contact near the rocker arm, put your ear to the plastic part of screw driver, do this for all the four axles, especially exhaust ones, if you don't hear a click click click sound, your valves don't have enough play and they will leak compression out and burn.
Combined with a bad carb setting or dirty air filter and all the above..it could do the problem.
My cylinder at 70 000 didn't even need rebore.

Or electric..
one + cable somewhere is torn by vibratiion/heat and makes contact to the chassi, will create parasites to ignition and it won't work normally on low charge, maybe.

CDI box.. I don't think so...but to be sure you could ask someone to try with theirs and see if it do the same.

Just some cable not giving enough contact due to oxidation; clean all with contact cleaner.

Short cut the security switch on side stand; put together the cables.

Good luck,
Let me know if you find it, would be knowledgeble,

Matt