Based on what I have learned so far, once the minimum set by the board is met, the important thing is to have a list of schools that are comfortable matches for the applicant. It's possible, even likely, that a candidate with SAT 1400 who listed MIT, Harvard, and Princeton may not get the scholarship since the PMS feel that s/he is not likely to be accepted into the schools, while another student with SAT 1300 with the schools like George Washington and University of Maryland - College Park, will be selected for the scholarship.
While getting better standardized scores will still help in that it makes the candidate better match for the SCHOOLS, it may be even more important to revisit the list of schools submitted, and see whether all the reachies are listed as top priorities, and safeties are listed at the bottom. Remember: the PMSs don't want to select, during early board rounds, candidates who listed their schools as a low priority (bottom of the list). My feeling is, you should list one reach, one match, and one safety as your top 3 choices on the list.