I think ‘Word of Mouth’ or finding out which schools others from your region have found good scholarships is a great way to find a hidden gem.
My daughter went to Wyoming and happened to live on an international floor in her dorm. There were several on exchange programs. Wyoming gives Out of State scholarships (which includes internationals) but ACT/SAT scores are required. You might find other state schools from the smaller (population wise) states that do the same, so look at Montana, Idaho, Nevada, Maine, West Virginia.
You just have to dig. And you have to accept that with a 3.25 gpa you can’t be picky.