Excellent post and well thought out argument. Let me attempt to respectfully disagree! :)
I think the government interest you describe above is in fact legitimate, not just seemingly so. The fact that government has corrupted its purpose (as the pursuit of power will always do) in this area doesn't de-legitimize that interest.
Outside of a few left wing “think” tanks, I don't think there's a legitimate argument against the assertion that children on average are more likely to become productive and law abiding citizens when raised by a Mom and a Dad. I would also argue, based less on data and more on personal observation, that children raised in such an environment also tend to be more moral people. Morality is the necessary corollary to small government (see my other posts on that subject). Thus I believe it is well established that a free republic like ours depends critically on a healthy institution of marriage throughout society in order to stay free.
The question is how to accomplish this. Indeed marriage is and should also be religious covenant, but we must keep government's role well clear of that aspect. As far as the government is concerned, marriage has one purpose only - to create an environment in which as many children as possible are raised in stable homes with a Mom and a Dad. Consequently, if a lefty church wants to “marry” two men and they introduce themselves thereafter as husband and husband, that's fine - but their union will not be recognized as marriage by the state because it doesn't serve the stated public interest of the institution. The state can therefore direct special consideration (not largess) to married couples such as first dibs on all adoptions, sovereign parental rights when determining how to raise their children (special protections from social worker busybodies) and other such things. In effect, the government approaches and provides protections to married families in much the same way we establish laws to protect businesses and intellectual property in the name of free markets, and the legal stability required for free trade.
As distasteful as it is for me to acknowledge this, it is a necessary role of government to regulate things. The trick is to make sure that regulation is aimed at the proper objectives: Justice, NOT fairness; liberty, NOT prosperity; individual freedom, NOT security. To the extent that justice, liberty, and freedom are served by fairness, prosperity, and security, then fine, but fairness, prosperity and security are NOT the objectives of government. Official recognition and protection of marriage and the family unit is an important part of that recipe.
The government does have the obligation to regulate things, but based on the fundamental law of that society. Our Constitution is based on natural law, and needless to say, “gay marriage” has no part in that!
The real interest of the state in marriage is actually not the social good of children, but property: who has title to it, how it is transmitted, and even who it can tax on that property.
Unmarried persons are free to leave their property to anybody they want to leave it to, free to hold it, free to give it away if they want, and certainly are available for paying taxes, so the state has absolutely no need to declare that they are “married” in order to pursue its interest in their property. However, if the state wants to create some system where unmarried persons (two gay men, or even something like an older parent living with an adult child) can apply for a “household” status, say, this could solve what gays claim to be the problem of unfair tax treatment, etc.
In other words, there is no need for the state to get involved in the sexual aspect of marriage; if they want to create some other practical institution, fine, but it’s not marriage and they can’t force the churches to accept it as such.
And gays have always had their faux weddings and other ceremonies, if they want to accompany the legal status with something more romantic, shall we say.
But that’s not what they want. They want to destroy the Church (and I include in that term other orthodox Christian churches) and they have seen that this is a way they can use the power of the state to do so.