I know a non-Mormon guy who married a Mormon woman and has kept her beautiful and desirable, by encouraging her religious involvement, even though he avoided Mormonism himself. Although it may indeed be a good idea to get out of this one, we all need to keep in mind that the situation is more complex than that. Honestly, I have given up on lds men as a single 25 year old. Please don't add to that grandious ego. Make arrangements to send her to your cousins town and let your cousin know she will be visiting. The thing is, even though no one else trusted my decision, I prayed about it daily for our entire relationship.
I got married to a Mormon woman. I believe in temple marriage, and in the importance of those covenants. He will eventually have more time for you, but right now he is likely giving you all the time that he can, even though it is very little. But his absence in the spiritual side of my life, and that of my mother, was very hard.
I think you need to figure out if you are willing to stay in a relationship with a man who's so busy, because trust me, it's not going to change anytime soon. No one appreciates how demanding it is unless they have lived it, many friends over the years said to me "lucky you, you are married to a Doctor. All i want to do it cry reading all of these posts.
Long story short, everyone is dead on. Going back in time, it was never encouraged for people to marry outside their faith and this covered most christian religions in the United States. I can't emphasize this strongly enough. Even after that, the Church discourages youth from entering serious relationships before they are considering marriage. Imagine if all the men in the world weighed over pounds and acted like slobs. Because people who have problems with interfaith families must needs shortly become a thing of the past. He is toning down his opinions and ocd ways a little, to be fair to him, I try to ignore the strong opinions, and him rearranging things.