Hi Andrew,
I think the problem comes from your priors – more specifically, a sigma of 1000 is usually way too flat for Poisson models (too be honest, I’m even surprised NUTS manages to start sampling, that’s impressive 
).
Indeed, because of the exponential link, values in the linear model become very big, very fast, so you need much more regularizing priors. If you do some prior predictive checks you’ll see this phenomenon very clearly.
For the same reason, I would use an exponential prior rather than half Cauchy for your err parameter.
Hope this helps 