it sure sounds like it’s flooded and getting way too much fuel. Shut off the petcock, full throttle and crank it for about 20 seconds. If it fires even a little bit then it’s a fuel delivery issue....normally yes, by bending the valve tab on float bowls, but the carburetor for the sixes are more complex Mikunis double barrels so don't know how easy is doing this. The level should be by the line separating the carb bodies and the bowls. If this level is too high, makes it too rich, if too low, makes too lean, difficult to start,......but am speaking in general, for motorcycle carburators,...I don't own a six, and I presume you don't have a factory manual which would tell you these details more precisely.
…..and I don't mean to send you away, not diminish the valuable inputs from the other members of this forum, we are all trying to help and interested in speedy solution, but must mention there is also a dedicated Kawasaki six forum Home with a lot a devotees to this engine, and a lot of direct experience knowledge, but please, stay with us and let us know how this goes.