Monogamy must be a choice

I would add one carrot to the stick: allow wronged spouses to sue for adultery. Both the other half and especially the Third Party. Make it easy to check online who is married and who isn’t. No excuses.

We used to, and it actually conserved the union. It’s a legal contract re fidelity. ENFORCE IT.

Marriage must retain its exclusive rights

I’d also ban an atheist from getting married. Get a partnership but marriage is a religious ceremony requiring a belief in God/s.