I hate to disapoint but much of your ideaological history of marriage isn't correct. Under Roman law marriage is a contract and therefore under government legal control but not so in Germanic societies where the legal issue is more about legitimate or illegitimate offspring. The Church and medieval society pushed marriage into cannon law courts to bring concubinage under control and most importantly because it was taking an oath so the validity of the marriage is bases upon the validity of the oath and therefore a matter of Church jurisdiction. Even to this day Roman Catholic theology and I believe most branches of the Catholic church deny the need for a priest or clergyman to be present at a marriage. The sacrament is make between the couple and God with the priest as witness. The move to try to enforce the priest upon the marriage was to reduce incidences of clandestine marriage which was largely eliminated in Europe during the Reformation except in England which did not do away with it completely until the 19th century, which is one of the reasons some states still have common law marriage because it is a remainder of clandestine marriages. Interestingly many of the same processes that brought marriage back under civil jurisdiction also reduced the rights of women.

In the end the issue boils down to this. Do you want to force change that is contrary to the legal principles of your society. That is always a dangerous road that almost always leads to a place where one is trying not to go when one starts down that path.