Many people tend to view me as a conservative chancer. You’re totally right that schools with sub-10% (and sub-5%) admit rates are extremely challenging to get into and are likely going to be a “no” for excellent students with high stats. But your profile would put you right into the thick of the mix. I think you should definitely consider applying to more schools that will meet your budget price without any loans. Because at those schools you’re trying hard just to get an admit, but then if you’re admitted the finances are okay. At other schools you might be likelier to get in, but then you have low (but definitely not impossible) odds of getting a full ride scholarship.
All that to say, you’re a very strong applicant and shouldn’t shy away from applying to any university based on the perception that you’re not a very strong candidate. Will think of additional options for you to consider, but I like @lilyesh’s suggestion of Lehigh for you.