I have been a mechanic for like 10 years for the record.
I had a very similar problem with my 03 636 streetbike.
When I would clutch up a highchair or spreader it would buck and hesitate. but not just at 12k rpm's it would do it at all rpm levels. But like your problem it would not do it in neutral and only under a load. It would do it on a sit down or ss but more on a tank wheelie. I dunno why but it did.
I tried changing everything. I had 3 other 636's to swap parts off to test.
nothing worked. you name it I changed it.
then my friend said "dude you got a problem with your wire harness I bet just change the whole thing and see what happens"
So I swapped the whole harness(its not that bad at all)
problem solved. Been riding it ever since with no issues.
I did save the old harness and planned on testing every single wire for shorts or continuity issues but I got lazy and never did it.
This may be your problem too I hope. later
