Another thing that will help speed up the model is parameterizing in the form of multi_normal_cholesky.
I posted a hierarchical VAR in that form where I ask about how best to weight the correlation matrices in that form at Weighted correlation matrices and cholesky_factor_corr . The original non-cholesky form was from james savage’s blog and you can check that out at https://khakieconomics.github.io/2016/11/27/Hierarchical-priors-for-panel-vector-autoregressions.html.