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Hi and thank you for your question.
Kawasaki does not use variable rate oil pumps on any of the 3 ZXI's they made in 1996 (750,900 and 1100). Therefore, the pump itself has no adjustment so it can't put out too much oil. About the only thing that comes to mind would be if it is leaking oil through the pump and that is where the extra oil is coming from. To test this theory, pull the small hoses off the oil pump, at the pump, (the ones that feed the engine, not the one from the oil tank to the pump) and let it sit. Watch the fittings on the pump to see if it appears oil is flowing. If it is, the pump has an internal problem and would have to be replaced or you can eliminate the oil pump and run on premixed gas/oil.
Another suggestion is to use oil that is advertised as low smoke or smokeless oil too. if the problem is really bothers you and the oil pump is not leaking, eliminating it anyhow and running on a premix of 50:1 oil would be an alternate solution. To eliminate the oil pump, remove all the components associated with the oil injection system and install an oil pump block off plate on the front cover of the engine. Cap off the fittings on the carbs for the oil lines and you are good to go.
If you have any more questions, feel free to ask.