Thank you both for responding! @jstanley I like your approach! I would worry a little bit about interaction between your fixed value of sigma and the inferred posteriors for err_lam, but I guess that is something that can be checked after the fact.
Either way, it’s good to hear that I’m not the only one trying to invent workarounds for the “issue”. As said, I would be willing to contribute this change to pm.Exponential, and perhaps other distribution functions, if people in the lead think this is a good idea and if someone more experienced is willing to keep a mentoring eye on what I do.