@Marian raises a good point, as what works best for one child may not work well at all for another kid.
By the time a kid reaches junior year in HS, the parents should have some idea as to what works for them, how to motivate them, etc. But a lot of parents are not ready to think about letting go, and they haven’t considered the thought that their kid may be able to take on some of this responsibility.
OP did not provide a lot of detail, but she mentioned her D is a very active and AP student. I projected on that comment to presume OP’s D handles challenges well, and that she may be more ready to take on some of this responsibility than OP might be willing to consider.
This morning I ran into a friend of ours who just sent her only child, her D, off to college. Since she was a couple years behind my pups, we had talked from time to time over the years, and she had asked me how I handled the search process, etc. I remember at the time listening to advice from my H’s older siblings about our nieces and nephews - our job as parents is to make sure we prepare them to make good decisions, but they have to make them themselves. Sometimes we have to be the parent, but they will get to the point where they may look to us as counsel instead. Another in-law told me to enjoy the college search experience - and pointed out that taking a day off for a college visit can be about the very best way to spend a day - it sure beats working, it’s all about hope and wonder and other good thoughts.
Since OP wanted to avoid coming off as too pushy, I was perhaps projecting that her busy D believes she is ready to handle this responsibility, the way that a lot of kids do. If so, then treating her D with more respect and patience might be a step in the right direction.