You definitely need to reach out to PIs during the application process. My husband has never had a grad student in his lab who didn’t contact him ahead of applying. He always does an informal interview with interested students before they apply or during the application phase to decide if he wants them before the grad admissions committee meets. In some cases, he talked the grad committee into accepting a student they would have otherwise rejected because that student had research interests/skills that my husband wanted for his lab.
You should also not be afraid to aim lower. Look at large state directional schools in your search. The most important factor is connecting with the right PI to make sure you get the lab experience you need and involvement in the right research project for your interests. Look at who the postdocs are when looking at labs, too (you’ll work with them more closely than the PI in many cases). The right lab at just an okay program can lead to excellent postdoc placement if you have the right PI mentoring you (you should ask where students end up doing postdocs at when looking at schools).