OP – Since Purdue is on your list, you might look at the Purdue Data Digest, here: https://www.purdue.edu/datadigest/; and especially the links to “Applications, Admits, and Matriculations” and “New First-Time Beginner Profile”. You can plug in your son’s stats to some of the interactive links on these sites, and perhaps get an idea where he might fall relative to recently admitted OOS applicants to Purdue.
In regards to potential NMSF money, my son – who graduated from Purdue in 2022 – received $250/semester for his NMF status; it was nice but not an overwhelming amount. As @momofboiler1 mentioned, Purdue is stingy with merit money, especially for OOS applicants. You might look at some of the schools that give lots of money for NMSF/NMF status; and you might include the University of Oklahoma on that list, as it awards some good NMSF/NMF money, here: National Merit Finalist Scholarship . The University of Tulsa has traditionally been generous with NMSF scholarships: National Merit Semifinalist Package - The University of Tulsa
I also second the suggestion of @tsbna44 for University of Alabama – Huntsville: solid engineering programs, plus the presence of the Army’s Redstone Arsenal and NASA’s Marshall Space Flight Center; and the U.S. Space Command will be moving to Huntsville, also.
Have you visited the campuses of any of the schools that you have listed, besides UIUC? Sometimes that will help you narrow down and weed out some of the schools on your list.