What does "for good" mean here? Does it refer to "a better way" or "forever"? or does it have double entendres?
Yes, you are partially correct. "For good" is an informal way of saying permanently, forever, or definitively. It does not necessarily mean that something has changed for the good. In the song, the singers are saying that they have changed permanently. Ex. The couple ended their relationship. They were done for good. Ex. The treatment was successful! Her father's cancer was gone for good.