PyMC: Taking advantage of sparse model structure in Adaptive Metropolis MCMC
This may be an unsatisfying answer, but it appears that PyMC3 has an example for a very similar hierarchical model: https://pymc-devs.github.io/pymc3/GLM-hierarchical/ Migrating your code to PyMC3 would give you access to newer samples, like the No-U-Turn Sampler (NUTS)