One can construct SNARKs from succinct MIPs, but these are again very different from deIPs. Sure, both SNARKs and deIPs involve highly efficient verifiers, and there is some overlap between the techniques used for succinct MIPs and deIPs, but that's pretty much where the similarities end. Furthermore, MIP based SNARKs are way too inefficient, and definitely not the ones used in Zerocash.

There are no constructions of SNARKs from deIPs, nor vice versa. In particular, one cannot construct laconic IPs at all for NP like languages.

P.S.: I'm Alessandro's student ;-)