Just caught up with and absorbed all of the above - thanks for all the brilliant suggestions.
This sounds reasonable to me, (daily_infections is just a constant multiple of unit_dS so no Jacobian adjustment needed) but I think it conflicts with the regularisation in:
unit_dS[2:no_days] ~ lognormal(log(unit_dS[:no_days-1]), beta_regularization);
There’s probably a way of doing both at once but I’d have to think carefully about how to achieve that.