Love a good process, Kaela A. and Zach H. can vouch for it!
Sharing what I shared with you, Cheyenne R., from another community here for others. My thoughts on it are:
Set the number you accept/support at 1 time based on the fatigue folks are feeling now to correct it moving forward.
Bundle them up so it's a “call for research participants” sort of thing that folks complete a form to share the needed info and select the program(s) they'd like to be considered for that are opening at that time. I'd imagine a cycle like this is on a quarterly or semi-annual one for folks.