where are you located? [roughly]?
The reason I ask is that I have had better luck with independent shops diagnosing and repairing situations like this than I have had at a franchised dealer. Often the dealer tech's experience is limited to maintenance, after market doo-dad installation and warranty issues, which in this day and age, come complete with a listing of wrench sizes and step by step process guide lines. Little need for investigative skills. A Japanese bike specialist might be the ticket.
I still believe your problems are in the carburetor. Achieving a balance. If you have a digital camera it might help some. Try to get us more history on this bike.....like, why was it parked way back when? Could there of been a mechanical problem, and they just walked away and left it sit? Are there any modifications on the bike that might lead you to believe that any jetting has been done? Is the air filter a Kawasaki air filter? Is the muffler a stock Kawasaki muffler? This is some critical information. If you have to pay someone to figure these things out, it could get spendy. They may opt to start replacing things until they hit on an answer. I don't like that to happen with my money. I like my money to go to gas and tires, not someone's guesstimate they bill for to the nearest decimal point.
Take a breath. Its only metal, plastic and textile. You can overcome it. Study what you are working with and get back with a detailed report of what you have.
“many a trip continues long after movement in time and space have ceased”- Steinbeck, [I]"Travels with Charlie"
[FONT="Century Gothic"][I]Sometimes your only available transportation is a leap of faith[/I] [/FONT]