I would reach out to the swim coaches of each school via email, and send your best times in your best events. Times are more relevant than one’s placement.
There is a lot of info on this website re: schools that have competitive swim programs. You may want to take a look at Suffield and Loomis, in addition to Exeter, Choate et al.
https://www.nepssa.org/2020%20championships/2020_championships.html