The best game plan for someone needing substantial FA is to have a hook. There are many hooks (geographic, URM, legacy, developmental case, etc). Since you can’t possibly change your race, legacy status or geographic location, there isn’t a whole lot.
EXCEPT for athletics. Most of the big boarding schools are always looking for top athletes to fill their sports teams. If you are a high impact athlete (meaning that you can start on varsity as a freshman, or that you have a really good shot at making a college roster) then this can make a difference when you apply. Especially if the coach really wants you.
The star athletes are always more plentiful for boys as compared to girls. There are also a few sports which schools find it difficult to get top prospects (who are also academically qualified): hockey, football, lax. There are also the sports which are not commonplace: water polo, squash, fencing, crew, sailing. Part of the reason there aren’t many top athletes in these sports are because of the expensive lessons, equipment and training required to excel. There are also some sports where good athletes are a dime-a-dozen: soccer, tennis, swimming, golf, XC, basketball.
So if you want to improve your chances next year (with FA): consider taking up a sport where there is a shortage of applicants. Keep in mind that most of these sports takes several years to become proficient enough to get a coach’s attention. You can’t just show up to the fencing nationals after taking a few lessons and expect to do well. But if you had to focus your efforts somewhere to improve next year, this may be one way. Good luck.