I'll bet you $10 (everyone is my witness!) that the springs on th espark advancer are sacked. The heat cycling has annealed them, making them advance WAY too soon. Nearly 100% of the engines I see now are this way (unless they have less than 5000 miles on them).
To fix: cut off first 1/2 turn of one spring, bend the end back out to hook into the weight again. If it gets better, do the other side. I have one spring minus 1 whole turn and the other minus 1/2 turn on my own K2, have for many years. Solves this problem handily by making the throttle much more linear. Mine had gotten so bad before I did it that pulling away from a stopsign, fully loaded with 2-up and 200 lbs of gear aboard was a dicey proposition! I didn't want to smoke my clutch, so I fixed my spark advancer instead. 
hey mark
hmmmm.... the advancer is a brand new 4into1 replacement
in a previous post about six months i said i had purchased a replacement spark advancer form 4into1..... because my original was missing some parts..... and this was your response
this is the thread:
http://forums.sohc4.net/index.php/topic,184496.msg2136383.html#msg2136383
in the last six months i have ridden the bike only about 200 miles.... so i can say its still pretty brand new
i did follow your instructions.
you still think i should do as you suggest? let me know and thanks for your help.
regards
Ah, the plot sickens...
The spark advancer I just bought from 4into1 had springs so strong that the engine wouldn't advance it even by 4400 RPM! This one is an F3 engine. The 'fix' for it turned out to be in using one of the new springs and one of the original springs on the advancer. It reaches full advance at about 3100-3200 RPM for a more linear throttle response against the lean-burn PD42/b carbs and the F3 cam.
The things that make it jump like that are usually an uneven mix of the spark advance and the fuel: what is physically happening is that it is lean enough at idle, then a bit too lean just above idle (this can happen for a number of reasons) and then too rich, This latter part is what makes it jump up so high in RPM. It can make it a nuisance to ride when carrying heavy loads, due to the 'quick' clutch closure this bike also has.
I tend to first lean out the idle (which I think you have already) and next to back away on the spark advance. The 2 ways to do this are:
1. Stronger advancer spring(s), so long as full advance can still be reached by 3000 RPM where the cam is coming on.
2. Retarded timing, at least for setup and tuning.
If you still have the original springs on the advancer from 4into1, and if they are like the one I just got last month, then what is happening is a buildup of unburned air-fuel mix in the intake tract from the timing being TOO FAR behind, that finally 'takes off' when the advancer reaches about 20 degrees (halfway up the curve). It literally 'clears its throat' right then, much like a dragrace bike with fixed advancer timing, and tends to hang at that speed until the unburned fuel clears away, then it falls back down to the lower speed again, all without moving the throttle. If you're in this situation, try one of the springs from your original advancer and one from 4into1 on that advancer as a starting point to see if it improves. The K2 engine's cam opens earlier than the later bikes (K4 and later), so the spring rate will ultimately need to be somewhere in between the OEM too-soft spring of the AD125 advancer and the stiff one of the 4into1 advancer. This can be obtained by trimming off 1/2 coil from the softer spring at a time and testing. Painful, but only has to be done once.
