Saving a '81 KZ750-E

Great looking bike and I love your garage / shop! 
Could you run a flexible vent pipe off your bike exhaust to the outside in order to test and tune in the cold weather?
 

The thought crossed my mind, but I have another bike project (and several non-bike related projects) going on, so I just switched to some of the others for the winter.

I still haven't figured out why I am being so procrastinate about doing this carb synch...  I got a fuel line long enough to use the stock tank, resting it on one of my wheeled wire shelves.  I can use the same wire shelf to suspend the gages.  I have a design in mind to make my own wrench instead of buying Kawi's special tools.  I have warmed up the bike again and verified that I have solved all of the fuel leaks in the lines and carbs.  Another nice point was I verified my tach is operating quietly now (one of the first test drive's problems).  I guess after sitting for 28 years some things require some lubrication!  Gotta finish the break in and post some video of it going down the road.  

Finally giving the Green Monster some love.  About frickin' time...  I removed the steering damper so I can figure out a better mounting method, and utilize the full travel (it was binding right before full turn on one side).  I also improved the amount of steering by removing some material on each side of the steering stops.  Having guessed at how much steering angle when it was only a frame, I left some extra material for adjustment purposes.  Moving the bike around is much easier now.  I also rechecked the float levels.  So it was time to start it and see how that helped.  Yeah, it's been too long since this bike got any attention - so much so the battery needs charging to fire it up.  

I am pulling the carb bank off again.  #2 cylinder is not running right.  It fouled the plug, which makes me think that cylinder is running rich for some reason.  Time to recheck the float levels and make sure the needle and seat are clean.  They should be as they were installed new during the rebuild, but you never know.  The carb sync wrench is arriving tomorrow - I was going to make my own, but found a really good deal online for one so I bought it.  Bound and determined to get this motor broken in before winter!

Getting a bike running is one thing. Tuning it is a another. Ergonomics, suspension, carbs, etc. Dialing it in takes time. 

First, Sorry for coming to this party late.
When I got my KZ750, PO told me #2 cylinder running rich. I traced it to the fuel valve. Gas leaking through vacuum line into the carb. I rebuilt the valve and it still leaked.
I ended up just swapping out for a Pingel valve. Problem solved.
I  wanted to bring this up before you start chasing the #2 carb. 

Thanks and welcome  Gertch , this a common problem of vaccum accutated petcocks. The rubber diaphram gets a crack and sucks fuel into the vaccum port.

I noticed a bit of a fuel drip with the tank off and the valve set to "on".  I tapped on the valve with the handle end of a screw driver, and the drip seemed to stop.  Later it was back again.  I did rebuild the petcock during the bike build, but sounds like a good place to eliminate a potential problem.  I will spring for a Pingle and see if that helps.  Thanks!

I don't know the spacing of the mounting bolts on the 750E's petcock, but the KZ/Z650's is 44mm center to center.
I bought a Suzuki petcock, new, from Z1Enterprises.
Direct bolt on, and has been working great for many years.
 

I am going to call Pingle direct with the bolt spacing on my valve to see what they have.  Their web site does not list any applications for my bike, so a call is in order.

Not sure but you might need to modify the tank. Pingle has a round pickup screen and if your tank has the oval to match the OEM screen then you will need to ream the tank some.