I don't know if your situation has cross-classified data or longitudinal data. If the former, we just posted a Psychometrika paper yesterday under Papers, Bayesian Analysis and we have a paper on this too:
Asparouhov, T. & Muthén, B. (2015). General random effect latent variable modeling: Random subjects, items, contexts, and parameters. In Harring, J. R., & Stapleton, L. M., & Beretvas, S. N. (Eds.), Advances in multilevel modeling for educational research: Addressing practical issues found in real-world applications. Charlotte, NC: Information Age Publishing, Inc. Mplus scripts.
None of these papers can be classified as application oriented - they are technical but have applications.
If your situation involves longitudinal data - see our upcoming Johns Hopkins workshop on DSEM and also our new web page
Usually, results are rather robust to non-normality of continuous variables as long as they don't show strong floor or ceiling effects. It is a research question how much that affects Bayesian analysis which assumes normality. You can do simulations in Mplus to study it.