Those overflows don’t seem to appear with NUTS so I wouldn’t like to comment on what’s causing them (though I can definitely see them too using Metropolis) - probably better for some of the devs to weigh in on this stuff, sorry!
Looks like there’s about 17% zeros in claims which may be enough to warrant the ZeroInflatedPoisson as the likelihood. That’s easy enough to implement, and you can compare the two models via az.compare to see which has better predictive ability. Looking at the spread of counts though you may want to try a Negative Binomial too.
I hope that helps!