I originally read that the fuel level should be set to the level of the float bowl gasket to which I set them using the clear tube method, carbs off the bike using a spirit level, etc. I then read in the manual that they should be set to 4mm below the gasket line. I have now done this.
Everything you are doing will contribute to a better running bike when you eventually solve the current problem.
In doing this I came across a worn piece of insulation, revealing bare wire right next to the frame. Maybe this was the cause of the intermittent stalling?
Perhaps. My own experience with worn insulation and bare wire rubbing inside head light shell was the cause of a blown main fuse.
While I was turning the engine over to get the clearances it made a hissing noise. I'm assuming this is not normal and is an air leak
You have some compression so this would be normal. You might find it easier next time to rotate crank with plugs out but not a big deal
Assuming your valve clearances are in mm then yes you have 3 that you need to address. Clearance should be .08 - .18mm I believe. The workshop manual will be invaluable and has a cam cap tightening sequence on page 55.
Some tips
Before you remove a cam shaft use a zip tie through one of the holes in the camshaft sprocket and around the cam chain so you dont lose sprocket to chain relationship.
Dont move the crankshaft until you are finished.
You may need to loosen or remove the cam chain tensioner depending on what type tensioner you have - check manual.
Remove cam caps as per age 55 in the manual.
Lift and roll back the camshaft +sprocket+ cam chain.
I use a magnet to remove the bucket and shim.
I always had to use a digital caliper to measure current shim size. Shim size is printed on new shims but i've never had an old one with print remaining.
Refer to the table in the manual to find out what size you need to give you the correct clearance. Looks complicated but once you do it and see it it's pretty simple.
Let say you do the exhaust cam first then I would put it back and put back the cam caps without torquing and then do the inlet valves same way.
I get kawasaki shims from my local dealer. They come in a package of 2.
Kawasaki.com owner info, parts diagrams etc will show part numbers to order.
When you finally put everything back together pay special attention to the torque values for the camp cap bolts. Specs are in inch lbs (104) not ft lbs. This is just a hair beyond snug using a short wrench and I usually go a bit less. Something like 8 or 9 ft lbs which is 84 to 96 inch lbs.
When you do have it running and warmed up it would be good to check compression like 650Ed suggested.
Hang in there. I bought my 750 early July and over then next few months found wiring burned and shorted from battery acid due to lack of a breather tube, Plugged pilot bypass holes in the carbs. worn float valves, an oil pressure sensor that randomly shorted. Took me 3 months to learn what I had and to get the gremlins out but that was 13 years and 50,000 km ago and worth the experience. Still have the occasional problem but nothing that cant be handled using common tools.