Thanks - work in progress.
Just a shot in the dark really, maybe the inlet should be cleaned? They have been left untouched for all of the 240.000km and the place they get most dirty is where the butterflies usually are - I now know that at least 90% of my riding is very close to 15 degrees. This theory corresponds well with the dirt I could see. I used brake cleaner, WD40 and carb cleaner
It helped!
Not perfect, but substantially better. Now it's a little annoying where it yesterday was difficult to ride (at least in town).
Since I now don't have any main suspects, I try to focus on how many and which of the small things it can be. Dirty inlet was one. Still is actually. I'm buying another spray can of carb cleaner - maybe there is more nastinesses in the valve area... Of course fuel filter is still on the list. Both because Howie suggested it and because I really can't NOT try a new filter.
