Stubborn cylinder #2 - Can't figure it out!

I'll try to keep this brief (unlikely). I've completely customize a 1980 KZ650 F1 into what you see as my avatar image. I've gone through everything, short of a total engine rebuild. I drove it all year last year and the first half of this year with little issue. However, one persistent issue I had was the exhaust header on cylinder #2 being at the same temp as the other 3. It didn't really bother me but now I'm obsessed with it and NEED to figure out why. This is mostly the case now as I'm trying to re-tune the carbs and the plug on #2 is wet, black, and oily. In fact today there was oily gas dripping from the exhaust drain hole. The other 3 are completely clean and/or slightly white. 

Current setup:
-K&N pod filters (I know, I know...)
-Rejetted (115 mains, 15 idle?)
-Aftermarket muffler welded to original 4-into-2 headers. Lightly baffled mufflers (cheap shorty ebay ones)

What I've done:
-New ignition coils
-New NGK plugs
-New timing condensers
-Timing calibrated carefully
-Carbs balanced to around 200mmHg
-Floats dry calibrated (not wet, don't have the little connector thing)
-Biggest thing: ALL 4 cylinders test right about 150psi consistently!

Last piece of info: after a ride home from work, headers on 1-3-4 are around 250-350 deg F. The header on #2 is around 150 F. So not totally cold. It seems to fire occasionally but not consistently? It also seems to fire only when getting beyond idle circuits and getting into the main jet throttle level. So my final thoughts here are to rejet the pilot jets with something bigger. 1-3-4 plugs are very white/clean at idle despite air screw basically being all the way in.

Thanks to those who read through all of this and have any thoughts for me!! I really hope this is a carburetor issue and not an engine issue! 

 

Check compression on all cylinders.
Replace spark plug.
Swap plug wires between #2 and #3
 

Sounds like a bad valve seal is fouling your plug with oil

........and that is where the extra cooling would be coming................but if so, he would notice oil level drop.

Since it is an 80 I would assume you have a vacuum operated petcock which runs off of the number 2 carb.  If there is a hole in the diaphram in the petcock it can pass more fuel into carb/cylinder number 2 which would make it rich and run cooler. 

Compression checks out across all 4. Would that rule out valve seal?

New plugs on all 4 and have swapped numerous times to be sure (incl wires)

Oil level seems steady but I can keep an eye on it

I did have a vacuum petcock but it became leaky so I got a different one. I run it on prime quite often. I did notice as I was balancing the carbs that the vacuum ports, the ones located under the couplings, had some gas in it when I took them off. 

Fuel in the vacuum caps is ok. I learned that from Swest. I had the same question.

A compression test will not tell you anything about the valve stem seals. All they do is prevent oil from running down the stems into the combustion chamber. Even if you left all of them out of the engine, the oil level would drop so slowly it would take a bunch of miles to see a difference. It does not take much oil to foul a plug or smoke up the neighborhood. A drop or two of fuel in those bottom vacuum tubes is normal. 

Different bike with a DFI setup I know but...

Had a similar problem with my GPZ Uni. Was getting lean/sooty plugs and wildly out of sync header temps and uneven tickover/running

Turned out to be very slight cracking inside the rubber head carb boots. They weren't visible until they were tightened and opened up which was causing an air leak as they weren't sealing properly against the head.

Drove me mad at the time trying to find the problem.

Anyways just a thought for something else to check!

I see you changed coils and plugs.
What about plug caps and HT leads?

Swop cyl. 2 plug wire with 3 and 3 with 2... you can do that and have the engine run just fine because it fires on the power and exhaust strokes. (You may have to un-mount the coil due to HT lead length)
 
If the problem persists, at least you will have ruled out the ignition system as culprit.

Has anybody tried using an overhead valve spring compressor on one of these engines?
 

Yes,
here's a vid I found that is obviously (not ) a kz650 but it has similar parts  that a 650 has and will give you an idea on how to use a valve compressor 

  (76) Valve Removal & Installation Method 1 : Valve Spring Compressor - YouTube