Hello!
I think the problem is that the your priors are too tight, and their influence dominates the data in the posterior.
Here is the same graph as that which you showed, except with draws from the prior:
As you can see it strictly excludes the data. In the model like this, the priors are going to play a much more important role in posterior than in, say, a large-N cross-sectional linear model.
Here is draws from the prior of the same model, with sigma=5 on both standard deviation priors, and sigma=10 for the standard deviation of the init_dist distribution:
After adjusting the priors, I get the following posterior for i_z[0]:
