Ok a lot of what you said went way over my head. I don’t think I have the wherewithal to fit the reparameterised beta-binomial in the way you describe. Perhaps a few years ago when I was more immersed in manually coding stan rather than using shells like brms, but it seems those skills decay if you don’t exercise them regularly.
But in a way what you say gets back to the thrust of my original post. Using model comparison techniques like loo-cv gives you a way of comparing models that is somewhat objective and sequential and where you know when to stop: when the next model doesn’t add predict anything any better you stay with the simpler model. But that process is predicated on being able to compare models, which you can’t do if you can fit the model in the first place. It’s a hard limit on model refinement. And it occurred to me reading your latest post that yet another hard limit is one’s own knowledge: I don’t know how to fit the reparameterised model you mentioned. I might have to start practising some radical acceptance of my own limitations, and that they may limit what I can do. Anyway thank you for your answers. They’re very much appreciated.