I suppose you asked only for advice on how to improve your chances, so I’ll get that out of the way:
Stress to the schools that you are absolutely committed to doing everything you can to help the XC and track programs.
As far as the SSAT score, the 84th percentile will not help you. Some very wise people on these boards will say it’s a fine score and you should submit. Perhaps I am not wise, but I would not have advised my child to submit that score. I think anything in the high 80s and above should be submitted for “top” schools. I think most of the Asians who get admitted to the “top” schools have scores in the 90s.
With all of that said, I ask the following: as a very religious Catholic, why would you want to attend Groton or especially Middlesex anyway, except that they are prestigious nearby schools? Perhaps I am making an incorrect assumption about what you mean by “very religious Catholic,” but I suspect you’d be a fish out of water at either school. Middlesex, especially, is extremely “progressive” and likely simply not a fit for a very religious Catholic. You may want to check out some Catholic day schools within driving distance of your home (likely many great ones in your state) or extend your boarding school list either to expressly Catholic schools or to schools that, while likely progressive, are perhaps not as extreme that way or are at least bigger and so more likely to have a few kids who share your values. In other words, widen your net to schools that are likely a better fit for you.