Sorry I won’t have the time to go into the nitty-gritty of your model, but since this has been here for a while I thought I’d chime in and maybe someone else can pick up where I left or correct me if I don’t get it right for your specific case.
I am assuming you tried just running what you implemented and you are getting the warning on the Jacobian correction for nonlinear transformations. I guess the summary about this warning is that when you transform variable and specify a distribution for it you have a different posterior from the untransformed one. But that may be ok, as long the transformed-variable posterior makes sense.
So an alternative parameterization of your model could be specifying the distances as parameters and placing the priors on them (you’d have to deal with the number of parameters when going from positions to distances, but assuming you could have a matrix of distances, it would be equivalent). If after all of that the model you end up with is reasonable, you can just sample from that, or you can go back to your original formulation, but knowing that what you are actually sampling from is the reparameterized model.