Hi John,
Welcome, and thanks for this detailed question!
Using Latent and gp.prior with a StudentT seems relevant to me, as shown in this example.
However, I think @bwengals will be able to help you more quickly than I on this 
Hi John,
Welcome, and thanks for this detailed question!
Using Latent and gp.prior with a StudentT seems relevant to me, as shown in this example.
However, I think @bwengals will be able to help you more quickly than I on this 