I am not expert, but I try to give my 2 cents.
seems to not be justified by your data, and in Stan is usually discouraged as too wide prior.
Are you sure you need the c paramter? There are a lot of degrees of freedom, here the parameters a and c play overlapping roles (maybe simplifying the link function could help). Is your model related to this?
If so can you confirm that you intend to use 1 - and non 1+ in your equation?
Why are you transforming these parameters with exp?
Furthermore you can read some non-identifiability problems from another post GLM with growth function - problem of indetermiinability when slope = 0 - #3 by stemangiola