Hmmm... well I like that Muslim women are modest mostly for starts, and men too, but that stems with all of the other things that are important to me. I remember somewhere in the Bible, if somebody knows the scripture I am talking about that would be great, it says women should have their hair or face covered in church. It also says that women shouldn't teach men. So in that case, it seems the Bible teaches the same thing, but a large amount of Christians don't follow it. I don't know why Muslims follow that law and Christians don't.
Actually there are many Christian churches where women are not allowed to be pastors, including the Catholic church. Women in the Catholic church were required to wear head covering until the 1970s and there's no reason why you still couldn't during a traditional mass, I think it would be looked upon more kindly at mass than during a Protestant church service. You could be a Traditionalist Catholic.
You could also become Eastern Orthodox or less likely Russian Orthodox, they cover their heads. I'd become Orthodox before Muslim, because to me your decision does not seem to be soundly based in theology, just with your concerns with what you view as immodesty or lack of conservatism in some Christian churches.
It's interesting that you're Lutheran, because Martin Luther actually advised women to continue wearing veils, they just don't in the West because of cultural trends.
One of the reasons I suggested the Amish was because to me they actually seem like the most similar Christian group to Muslims in the United States, not just because of modesty and structure, but because they literally live apart from modern ways, and this living apart from modern ways has had a heavy influence on Islam in Asia, which is why you see such conservatism coming from there.
And clearly, that kind of thing also has its downsides.