You asked how to increase merit chances at schools such as Duke and Vandy. I will discuss two students who I know.
Student #1 is a Robertson Scholar. Her objective stats were high, but not as high as your sons. She started a club at her HS and the club increased to the national level. It is now in schools throughout the country and she remains involved with all of them.
Student #2 received huge merit to Vandy… She also had high stats, but nothing like your son. Your son’s stats are higher. She had leadership positions with several high profile, national volunteer organizations She took her leadership to one of the morning talk shows, This girl turned down Vandy to attend a higher ranked school.
It seems to me that the big merit to these schools is very often based on things other than stats (my guess is that stats get you an initial look). I don’t know the specifics of your son’s ECs and how they compare to those who received big merit. As noted above…it doesn’t hurt to try. You indicated that your son has research experience. Has he been published? Has he presented his research anywhere…maybe at a conference? I actually know a student who presented his very personal research to Congress (he wanted to increase funding for a specific disorder).
My D applied to some schools that are of interest to your son. My experience is that the vast majority of people who don’t qualify for FA should expect to be full pay.
The good news here is that you live in a state with amazing schools, and there are a whole bunch of schools out there that would offer your son merit. Congrats and best wishes!