Have you tried fitting a simpler version of the model? Perhaps trying 1 week, or a smaller weight dimension? Or hard coding the week specific/treatment effect terms rather than generating them? Maybe try to simulate 10 000 people with all the same qualities?
That’s usually illuminating for my problems. Sounds like there are lots of moving parts in your machine which could all go wrong in some way.
My understanding is that, in the Bayesian sense, data and parameters are the same thing so there shouldn’t be an upper bound.
If the priors are extremely informative, have you tried sampling from them to see if the results look sensible?