Hi, we know cross validation and model comparison can be tricky because in many cases there are several correct ways of comparing the models. We are actually working on some resources to help with that, they are still a work in progress, but it should be useful already. Here is the notebook covering multiple likelihoods. The link is to my fork which has the open PR, feedback will be most appreciated. You may also be interested in the other notebooks of the section: https://nbviewer.jupyter.org/github/arviz-devs/Exploratory-Analysis-of-Bayesian-Models/tree/master/content/Section_04/
Having said that, there is also this example in R which I think will be much closer to your model and could also be helpful: Cross-validation for hierarchical models
I will try to read this topic with more time to see if I can help further. I think this multiple measurement and multiple subject models are ideal to teach the nooks and crannies of CV.
By any chance, do you know about some public dataset other than the rats one with similar characteristics?