If prayer in the classroom bothers you, you might not like it here and should look into going somewhere else. As far as those who don't have an ecclesiastical letter writer - a few of my classmates just found someone who filled that role in their life. Is there someone you would talk to about personal matters and seek advice? It's mostly a character reference so just do the best you can.
The only way the "spreading the gospel" mission will affect you is this: LLU has (in my opinion) the best service program around. They do dental mission trips all over the world between quarters and during the Christmas and Summer breaks - the student pays 1/3 of the travel cost and the alumni/wealthy church members pick up the rest of the tab. Although I haven't taken advantage of this yet, my classmates have been to Madagascar, Costa Rica, Fiji, etc. - all kinds of cool places.