I think you have misunderstood my proposal. I cant see any real difference from yours:
civil unions without discrimination conferred only by the state and providing all legal rights and obligations. “Marriage” optionally provided by clubs, cults and religious bodies, conferring recognition and responsibilities defined by that organisation – a civil union being a necessary prerequisite. The name should be what it is: civil union, or Catholic, Lutheran, Hell’s Angel; whatever “marriage”. The generic term "marriage’ would no doubt be used on most occasions but would have no basis in law on its own.

There would be no government “meddling” with religious marriage and no discrimination on the civil side: except for: identification; a minimum age limit; anti bigamy provisions; and possibly citizenship (I haven’t thought that last one through yet).