Hi Mike,
Yeah I think the problem is partly coming from some of your priors: maybe try Exponential instead of HalfCauchy for your sigmas (still fat-tailed but less than Cauchy). The sigma of mu_channel seems really high too, especially for a slope. In general, you need much more regularizing priors with hierarchical models, especially for a model with so many levels. I think prior predictive checks could help you here.
I wonder though why you’re modeling four levels if your real data are not actually hierarchically nested, as you said – from what I understood however, your simulated data seem to be hierarchical (b depends on b3, which depends on b2, etc.).
Maybe what you’re looking for is modeling 4 different clusters in the same hierarchical layer? If that’s sounds interesting, here is a thread discussing it, and a notebook implementing it (code 13.22).
Hope this helps 