I have a '91 Zephyr 750. There was a Zephyr Zone Forum, but it is currently down for 'maintenance'.
I have the Kawasaki factory manual, and also the Haynes. They show all the things you would need. Regularly, they are available at Ebay. Just search: Kawasaki Zepnyr
The carbs should be Keihin CVK32s. My manual actually says the mix screws shoud be 2-3/4, assuming your carbs are clean, in good shape, and stock. I have them at 3-1/2 and a K&N filter is the only non-stock item.
There is no preset on the idle screw that I know of. Other than measuring before disassemble. Once the bike is running and warmed up, it is easy to adjust it, to about 1100-1200 rpms.
About the synchonizing; of course, you need a synch gauge, preferably a Morgan, or one with metal rods, but some people make sure the amount of light is same thru the butterflies, before mounting the carbs, to get them close. The float levels is something you should have checked also. Your post does not indicate you have cleaned and inspected the carbs, other than replacing the bowls gaskets.
There are two big hoses that are bowls vents that run backward and down, connected to nothing. The vaccum nipples of carbs 2 & 3 go to a "T" and the fuel petcock. Nipple of carbs 1 & 4 to the vaccum valve to reed valves on the valve cover, that feeds fresh air to exhaust ports.
The Keihin CVKs dont have 'choke' plates, they are really enrichener plungers. The engines are hard to start after not runing for a few weeks, and the 'chokes' have a on/off character. Without careful, and I mean real careful modulation, the engine will run to 6K rpms on full 'choke'. It is hard to find the right spot, specially after a long period of not running.
My bike is almost 20 years old, and has been very reliable with proper care and sensible moderate riding. Don't know how many miles, abused, or neglected you bike may have been, or wheather you have checked things like compression, valve clearances, spark plugs, and coils.
Hope this help.