Personally I don't really mind who does or doesn't get married unless it involves being a parent, because there is good evidence relating to that.
What surprises me is an argument that claims to be based on justice/fairness but whose demanded alternative simply widens the beneficiaries of the injustice. As you have noted, there is a very obvious and undeniably fair solution: simply do away with the legalized reference to marriage. Revert to common law/civil contract, which purportedly is all "marriage" really is according to many proponents for change. In that case the label can be preserved for people who value its traditional/cultural meaning and everybody else can push for whatever common law or civil measures they please.
Surely that's the obvious solution- unless there is value seen in forcing a change to the institution of marriage?
"... They ne'er cared for us
yet: suffer us to famish, and their store-houses
crammed with grain; make edicts for usury, to
support usurers; repeal daily any wholesome act
established against the rich, and provide more
piercing statutes daily, to chain up and restrain
the poor. If the wars eat us not up, they will; and
there's all the love they bear us."
-- Shakespeare: Coriolanus, Act 1, scene 1