I don’t think it is out of line to ask the LoR writers if they wrote about OP’s interest in Bio. That is different than asking them for a copy. If these teachers are “mentors”, they want to maximize the OP’s chances and I doubt they would find such a question offensive.
Also, I don’t think LoR writers are so uniformly concerned about students reading the LoR’s. I have written numerous LoR’s for law school and business school. I wouldn’t take on such a task unless I felt strongly about the employee. I always offer to let them read my draft in case I missed anything they wanted me to cover. I am their advocate, not a judge. I don’t doubt though that HS teachers who have to write multiple LoR’s are more reluctant to allow students access to their LoR’s since students may compare them or pester them for changes, so definitely if the OP signed a FERPA, I would not ask to see the letter itself.