By separating marriages in the eyes of godless caesar from marriages in the eyes of God, you make this a hard question to answer. Some of us might have different answers, depending on which category of marriage we are talking about.
I used to agree with you that the church should separate these into two categories, but the more I saw the ramifications, the more the idea of two standards came to trouble me. The place where two standards clashes is a place I know is of concern to you. If the church judges some marriages legitimate in the eyes of caesar but not in the eyes of God, will the church then work to break up those marriages? I know you oppose those in the "standers" movement who take it that far.
The commandment, "Thou shalt not commit adultery," is not only for the married person, but also for the neighbor of the married couple who is called upon to respect his neighbor's marriage. The more we do to make marital status uncertain, the more we undermine the spirit of this commandment. This is a problem with every system that refuses to recognize some marriages.
The principle behind "Thou shalt not commit adultery" is that we must respect both our own marriages and our neighbors' marriages. If I begin to think of my neighbor's marriage as less legitimate than my own marriage, I violate the principle of this commandment just as much as if I lust in my heart.
I find some of the arguments presented here more persuasive than others. Those that refuse to acknowledge the reality of some people's experience I find least persuasive of all.