I don’t actually think this is impossible, but it definitely depends on the level of the student and what level of school they are willing to attend. If the student is highly competitive, achieving this level of scholarship is certainly possible. My son reached this level at 4/5 places he auditioned, though 2 of these are always tuition free. (Ironically, the one place he did not get that much was his safety school. Go figure.)
If the student is less competitive, you will likely only achieve this if the student auditions at programs that are slightly below level. It’s hard to tell from your list, but I am guessing places like state schools and some private schools more known for scholarships (in my city, DePaul and Roosevelt are good examples) would be closer to what you are looking for financially. You become a big fish in a small pond, and become highly desirable.
However, there are potential cons to this. While it is certainly possible to find great teachers at lower tier institutions, you still miss out on some of the opportunities of a higher tier, better-fit school. These would include better instruction (generally), networking, and also peers at a similar level who will challenge you. Sometimes it is worth pushing the finances a bit because you will get bigger gains in the long run.
Also remember that many kids start at a lower tier school and go on to a more prestigious graduate program. That is always an option.
Also, if you put a lot of effort into it, you can often get outside scholarships to make up the difference. This requires quite a bit of research and a lot of paperwork, but I have known students who were able to easily make up $10K or more with outside scholarships.