I realize you likely already recognize this, but in case somebody comes along trying to figure out how to parameterize a positive vector that sums to Z, a simple option is to parameterize in terms of a simplex and Z, and then to express your prior as a prior over the simplex and a prior over Z (assuming it’s acceptable to write down a prior in which Z is independent of the simplex), thus avoiding the need for any additional Jacobian adjustment beyond the one required to yield the simplex.