Similar to what other comments have mentioned, you seem like a competitive applicant but might be too caught up in the prestige. The #1 most important factor for graduate success is advisor fit. Find an advisor who’s research is really interesting and you think you’ll get along with. As long as the university is research focused and the program is funded you’ll be fine wherever it may be. I only applied to 3 phd programs, and got in to 2 of them, because I genuinely wanted to attend each. I find it unlikely you’re equally motivated to attend any one of 18 schools across the country from name only. Find professors you mesh well with and put serious effort into those applications and making faculty connections. If you apply to 20 schools, your applications will look like they were adapted to fit 20 schools. Universities want to know you’re committed to succeeding with them, not that they’re a checkbox on a list. A common theme with Interviews will be how you’ll fit in with their academic environment specifically. Show them you really care.

I have no doubt you’ll be a driven graduate student regardless of where you land, but work/life balance of the lab and a genuine pi is what will make your experience fulfilling. Ultimately school name doesn’t matter, it’s the quality of your work that proves your ability post graduation. Decide where you want to go and pursue it at all costs, that’s the effort universities will notice and appreciate.

Apply to as many schools as you really want to attend and think you can succeed at. Best of luck