ETH incorporating a SNARK verifier opcode seems to be quite likely,

July 2016:baby ZoE or ZeroCash over Ethereum
https://z.cash/blog/zksnarks-in-ethereum.html
https://github.com/zcash/babyzoe
"In our work this week, we extended the Ethereum contract language to efficiently support verification of zkSNARK proofs. Specifically, we added a snarkverify precompile (like an opcode) to a fork of Parity which uses libsnark to verify generic proofs."


Jan 2017: ZCash integration into Ethereum Blockchain
https://blog.ethereum.org/2017/01/19/update-integrating-zcash-ethereum/

Feb 2017
https://medium.com/@VitalikButerin/zk-snarks-under-the-hood-b33151a013f6

I believe the issue being of the Zcash private transactions are quite expensive in gas
in the context of executing on EVM. You mentioned Could the following fix or alleviate any of such issues?
Hawk seems to have a decentralized manager who receives inputs from the Users and produces the snark proof? correct?