The results of the tree depth investigation (I dropped the draws to 100 and tuning to 1000 down to save time) is that they came out as 6s:
Which is still somewhat high so is a contributing factor though again probably not your sole issue. Actions for tree depth is that I think you can do some tweaking like reparameterisation is usually a big one, you already have quite high tuning and that action didn’t fix my one and the long runtime you experience mean it probably doesn’t help your model either. You can lower the max tree depth as an argument but it means your exploration is less efficient and I think results in biased inference so not ideal.
Edit: I have just realised that increasing tree depth doesn’t necessarily mean it will take longer, since a smaller tree depth during the tuning phase means the sampler will adapt to what it sees and by exploring the full distribution during tuning can lead to more efficient sampling for your draws so actually I’m not sure you would need to edit tree depth at all and your are better off looking for improvements in other aspects