I meant standardizing after taking the log (and using a normal likelihood in the log-data) which would be equivalent to using the lognormal likelihood in the natural data. I just suggested this because you seemed interested in standardizing your data, the only advantage is that may help with choosing the priors or comparing multiple predictors which doesn’t seem to be relevant in your example.
In practice it should give very similar results to the lognormal yes. Again I suggested this because you were toying with the t-student in the natural scale. Not because I think it would be any better. I was just trying to understand why you were justaposing the options <lognormal + raw_data> with <student + standardized data>, which sounded to me like two orthogonal issues.
Perhaps to be more helpful I would ask how do your log-residuals look like? Do they look like they could be well explained by a normal / t-student? If so, then the log-normal or (log-student) would look sensible. If not, you may try other kinds of transformation or likelihoods.