This sounds like air idle control problem . Considering the mileage, carbon builds up in the controller causes the idle to fluctuate, I have not experience in the Z cause I only have 18k on mine, but had this on problem on my suv, The controller located on the throttle body was replaced, I also read you can clean it, like you use to do with the EGR valves, It depends how much carbon has built up. You have to reset the controller position once you remove it, there is a parameter that has to be set with a volt meter.
Good luck
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