Neal's funnel on a simplex

Hi everyone, I’m trying to fit a hierarchical model that involves a Dirichlet distribution over an array of simplex[3]s, and I’m running into issues with both divergent transitions and hitting the max tree-depth. Given the hierarchical structure of my model and the type of issues I’m facing, I’m wondering if I’m running into a simplex-version of Neal’s funnel. Are there any suggested ways I can reparameterize my model to avoid the funnel effect in the context of a simplex?

The relevant part of my model is roughly like this:

parameters {
  vector<lower=0>[3] population_params;  // Gets an improper prior.
  array[N] simplex[3] group_params; // Each simplex gets a Dirichlet prior below.
model {
  for (i in 1:N) {
    group_params[i] ~ dirichlet(population_params);

A potentially important detail is that in the context of my problem, it seems as though the true values of the group params are often roughly [0.5, 0.5, 0]. In other words, the posterior density is shoved up against one of the boundaries of the simplex, and this is actually a scientifically valid and important inference.

Any suggestions on how best to proceed would be very helpful!

I think @Bob_Carpenter is the resident simplex expert here