I know the mission is deeply meaningful...I think everything that makes me prepared to succeed in law school is directly attributable to mine. My first PS draft was about my mission. I went to great lengths to ensure that it wasn't cliche or rote, but that I talked in detail about my personal development. Still, I ended up scrapping it in favor of another, which only mentions the mission in passing.
I don't think a mission PS is off-limits, but it would have to be unique and powerful, and I would recommend one or the other (PS or LOR) related to the mission, not both.
Best of luck. Are you at BYU? I should hook you up with my sister. She's a nice young lady. Then all of the males in the family can talk about nothing but law school at family gatherings and drive everyone else crazy. (My sister and her husband are going to UVa law in the fall.)