How do I find where a Dimensionality error is when I can't graph my model?

This is fine. Coords and dims work in multiple dimensions:

coords = {'day':np.arange(7),
          'city':['Berlin', 'London', 'Tokyo']
         }
with pm.Model(coords=coords) as model:
    mu = pm.Normal('mu', 0, 1)
    # shape
    #normals = pm.Normal('normals', mu, 1, shape=(7, 3))
    # dims
    normals = pm.Normal('normals', mu, 1, dims=('day', 'city'))

    idata = pm.sample()

But I don’t see any instances of multidimensional parameter arrays in your model (though I may have missed it).

As for the shape error you’re getting, it’s not clear to me what is happening because many things have changed between the two models.