Horizons Unlimited - The HUBB - hesitations between 4500 and 6000 rpm (950 ADV)

First I had a leaking water pump and incompetent mechanics who took my front cylinder apart instead of fixing that...Than it ran, sounding as a one-cylinder (to me, but the mechanic meant it was ok)
Another mech blamed it on the dirty airfilter (which had about 6000km on it) and on a rubber cap that closes the airfilter box, where others have a part that I am not really sure what it is called...). He replaced the filter and took off the rubber and meant it was all good!
Then I rode a little faster after for the first time after that the first mechanic had taken the cylinder apart and noticed hesitations.
Back to the second mec, he did not believe it before he saw that the bike spit out quite an amount of coolant. Then he took off the carbs and cleaned them. Not sure if he set the jets any different.
No improvement.
After some days the valves were finally adjusted (very necessary!). Rode off to Mexico City (about 400km), problem still there. Mechanic nr.3 seemed to be a good one. We did a lot of different things, adjusted the valves AGAIN (necessary! the other guy had never done it before and did not have a lot of shims to chose from!)
He said that the spark plugs were dry and changed the setting of the jets. Still hesitating! He said it was just because of the altitude and the bad air in MC...cause he meant that they were adjusted for an average of the whole trip (sealevel-4500m). I did not really believe this but tried to trust in him. When I got to sealevel it got even worse...

I have tried different things but the problem remains.
I thought it was because of a crack in the intake boot of the front cylinder. I glued it and it got better but still...I had a bad contact in the ignition lock, took it apart and sotered it twice. Not better!
I bypassed the ignition lock with a wire and it worked fine. Then we put a switch on that point and the problem was back. Maybe it was not properly attached?
I found a melted contact between the regulator and the main fuse, took it off and connected the cables directly, not better.
I checked the fuel filter.
I replaced the fuel pump with a mechanical one,did not work at all.
I checked the spark plugs, took pics, the mechanic says they look ok...?
I am not sure if that could have any effect but most of the screws that hold the lock of the airbox down are not working any more cause the plastic is worn and does not hold the screw any more.
When I take off the tanks , I can see that it is quite oily in the air intake (that you have to screw out to take off the airfilter) of the front cylinder...To what degree is that normal? BTW this part has one tooth less which should hold it in place! I guess it broke off , I really hope that this part is not in the carb or in the engine!Could that cause a unregulated intake of air?
The last time I checked the (new?) airfilter after only some hundred km it looked dirty. Same thing now after mabe 1000km ???
I checked the fuel filter.
Could it be some setting of the carburetor or a pinched tube?
Maybe I should try to bypass the lock again, with a wire...
Could the regulator have any influence?
The battery contacts are ok on both sides.
Could overheating or mal-lubrification (cause of water in the oil) have caused any changes (with the valves for instance) that could cause this problem?
Is it possible that the fuel pump is starting to get bad and only works improperly in the mentioned rpm range?