My son’s high school (Top 25 in California) has a lot of kids going to UIUC and UT-Austin. Last year’s graduation class had 15 go to UIUC and 5 go to UT. So even though some OOS public schools do prioritize their students (which I agree with), high achieving OOS students will find a place.
It’s true that UT has to take the top 8 percent of Texas students, but the engineering is top rated. A&M as well. I would personally consider those schools over some UCs.
Arizona State might be a school to consider. With your son’s stats he would get into the Honors College with a pretty decent financial package. Definitely warmer than St. Louis now. I need to make sure the kid packs enough winter clothing when he returns to WashU next week!