Definitely get recommendations. A rec must be written by a member of the sorority to which the rec is being sent, so that's women from 13 sororities you need to find. SOME sororities allow collegiate members to write recs (they must be from another chapter than the one at your school), but ALL of them allow alumnae from any chapter to write recs.
You may have friends in sororities at your old college or friends with whom you went to high school who joined sororities. If there is a chapter of a friend's sorority at Mizzou (and they allow collegiate members to write recs), ask her if she would be willing to write you a rec. Ask high school teachers, sponsors of any activities/sports you participated in during HS, friends of your mother/sister, women you know from a place of worship, etc. Often, when you find one sorority woman (even if there is not a chapter of her sorority at Mizzou), she may be able to point you in the direction of others.
Recs from women you know personally are best, but it may not be possible to find a woman you know personally from all 13. Once you've exhausted all of your personal contacts, contact the
Alumnae Panhellenic in the city nearest your hometown.
Good luck to you!