Joseph,
I will look at the case that you cited. However, I am pretty sure that no court has held that anti-polygamy laws are unconstitutional. Many years ago, the Supreme Court held that they were Constitutional. And although that holding is shaky in light of recent Supreme Court rulings, it has not yet been overruled and therefore remains the law of the land.
As I stated above, I believe we pasken (I will track down the Rama) that dina d’malchusa applies to all laws of the land (so long as they do not require violations of halacha).
You are right that if you simply live with them all halachically but only claim, legally, to be married to one of them, it would be permitted in many states (not sure about New York).