Thanks for all of that @brandonhorsley, super insightful.
I have been using numpyro instead of NUTS because it seems to be faster.
I have tightened up the priors on my model and also reparametrised the exponential scale parameters to be half normals. This has cut the sampling time down to 8 hours which is a huge improvement, and the r_hat values are looking better. Not where I want them yet, but much better. I think my next step is to pass more specific priors, rather than a general prior for each variable. Some variables I know to have a much stronger effect than others.
Perhaps I can run the NUTS sampler on a cross section and see where the pinch points are, as you say.
Thanks again.