Looking at the code you’ve posted more carefully, I honestly don’t understand what’s going on, so I retract my suggestion. I wrote out some code for a CustomDist for loc-scale parameterization of a LogNormal in the first model, but now I see you’re not actually providing data there and the parameters are fixed. It’s fundamentally not a generative model, so I guess you’re locked into using Potential.
Same goes for the second model. The data are being used as parameters of the normal – why?