I don't think circuit depth matters for SNARKs? Though there are other proof systems where AND depth matters. Also, though I haven't read the CODA paper either

I don't think circuit depth matters for SNARKs? Though there are other proof systems where AND depth matters. Also, though I haven't read the CODA paper either, I think they would only need a single fixed circuit containing a SNARK verifier. Since for a given security level, SNARK sizes and verification steps are constant.