1978 kz200 w/keihin pw26 rich idle no matter the settings

As the title says, kz200 with keihin pw26, no matter what I change the idle is still super rich. It will run fine at idle for a couple minutes, then get rougher, then quit completely. After it quits I pull the spark plug and it’s completely sooted over. I literally cannot think of anything else to check/change.
Things I have done:
Valves, point gap, and timing statically checked
Replaced carb boots to head and airbox
Cleaned carb (ultrasonic + blown out w/compressed air)
Brand new air filter, oiled correctly, stock airbox
Swapped idle jet 1 and 2 sizes lower
Swapped main jet 1 size lower (ordered more for tuning, smaller and larger)
Needle is currently set at the top (1) position and gives good off idle transition (this seems wrong, like everything is too rich?)
Set float height at lowest book value (28.5mm) and confirmed with clear tubing test
Battery is charged, have tried also running with jumper pack hooked up to battery, with no change
Plugs are brand new NGK B8ES gapped correctly

Any help is appreciated.

High float means low fuel in the bowl. You might want to try going the other way around.

Nessism wrote: High float means low fuel in the bowl. You might want to try going the other way around.

This is a :Facepalm: moment...I will check this tonight and adjust the float height to highest book value and see how it goes.

Did you cure your rich idle?
I have the exact same situation where my timing is set perfect, I  have a number 35 pilot jet which is the leanest you can buy, a 110 main jet and stock needle that has the clip set on second notch from the top which is just one step lean from stock. The bike idles fine when you start it up but then after fully warmed up, it dies at idle, giving it a black sooty plug. 
When running out on the open road half throttle to full throttle it seems to be running fine and when I do a plug check there,  the color is perfect.
Again, the carburetor is perfectly clean, float level set with tube method , valves set cam chain tension set timing is right on with a timing light. 
Sometimes when they come to a stop,  the rpm's rev high  like a lien condition and then comes back down and dies from a rich condition ! 
I just don't get it.

Something seems wrong with your pilot circuit.
Is your choke plate closing at idle?

I seem to be making progress.
I went from a 110 mainjet down to a 105, idle jet from an aftermarket Keihin 35 to a genuine Keihin 35, (bleed holes of genuine jet definitely smaller ) Needle jet clip set to leanest slot (top)

No longer a sooty black spark plug , bike holding idle after warmup so far.
With bike at idle, when I slowly roll open throttle it wants to die, so my transition from idle circuit to mid is lean, so moving the needle clip down a notch should clear that up.
Lesson learned ? This particular antique carburetor (Keihin PW26 ) in my experience is sensitive to oem jets and all jetting circuits working together , ie,
the circuits seem to overlap one another more than reported in the kawasaki service manual and on many carb tuning blogs/sites.
Especially the idle and mid range circuits.
Thank you for all input.

No luck still. Runs fine during warm-up and off of the idle circuit but once it gets hot it will not hold idle... it'll soot the spark plug and die. 
I do have the proper jetting I can attest to that after all the different combinations in jetting I have used it is now back to completely stock genuine keihin jets.

My problem ended up being worn cam bearing surfaces in the head, which was affecting the timing and valve opening/closing/duration. Something to check if you're still having this problem.