I am also not a big fan of “shotgunning”. I think that the highly ranked universities are looking for students who are a good fit for them, and if you have an honest and compelling answer to “why is this school a good fit for you” that is likely to improve your chances of admissions. You are also going to need to write a lot of essays if you apply to 20 or more universities, and I do not understand how you could do a good job on all of them.
You might want to first send in applications to 2 or 3 safety or likely schools (including ASU), then send in applications to a few highly ranked schools which do not consider your freshman year of high school (Stanford comes to mind as a good example and a great school), then perhaps pick 2 or 3 additional schools to apply to first based on just where you want to apply to – which schools feel right to you.
At that point you might have 8 or 9 applications in. Then think about whether there really is any point in sending in any additional applications, and prioritize whatever applications remain.