That’s what I feared 
I came across a version of this notebook but am only starting to look at it in details. Great idea to go and pin-down where the divergences occur (in my case that won’t be easy because of dimensionality, AR(1) processes and LKJCholesky are involved among other things!). If anything interesting I’ll report back here. Otherwise I’d say the question as originally formulated is resolved.
Thanks for your replies @daniel-saunders-phil and @cluhmann.