Hi, in these types of situations it is highly unlikely that iterating longer will help you much - there is most likely a fundamental problem in your model and/or its (mis)match to your data.
My best guess is that the model is just too complex to be informed by your data. How many datapoinrs do you have? How many replicates for each level of z?
In any case I would start by simplifying the model and trying to find the most complex model that samples well and the simplest model that causes problems. Some of the advice at Divergent transitions - a primer also applies to problems with high rhat.
Best of luck with your model!