Muslim American is a contradiction in terms, an oxymoron. You can be a Jewish American, a Christian American an atheist American but a Muslim is a Muslim PERIOD.
I agree with you about 95%. The problem is that you are using the wrong term to describe the invaders.
The word "muslim" sounds like the arabic word for "follower of God". Obviously this is wrong.
The word "moslem" sounds like the arabic word for "evil person". Seeing as islam commands it's followers to lie, steal, rape, and murder, I would say that "moslem" is a far more accurate description of them.