So off hand, I am not sure I understand what you are doing in terms of size/type of university. Meaning if a private college like Yale is your first-choice, with about 6500 undergraduates, it is not obvious to me why so many of your matches and safeties are much larger, and mostly publics. Alternatives could include somewhat less selective private research universities more similar to Yale, and also possibly stand-alone liberal arts colleges (although those could be too small for you, depending on your preferences).
Of course the sticker price on those alternatives can be expensive, but so is the sticker price for Yale. So you have to check NPCs. But an additional intriguing possibility is that with your qualifications, you would likely be in the running for merit scholarships.
So at least in my circles, common options to explore for applicants like you with Yale-type schools as top choices would include Case-Western and Rochester, which both have quite a bit of merit aid, and of course are R1 universities with similar-sized colleges. This is outside my normal “jurisdiction”, but I understand that is true of Tulane too.
More of a reach, but also a common option to explore, would be colleges like Washington University in St Louis, which also has a lot of merit aid (and just a lot to commend it in general). Again, not that popular in my area, but a college like Emory might also fit into this category. I understand you don’t really need or want more reaches, but I think for applicants like you, putting yourself in the running for merit scholarships from colleges like that can sometimes work out really well.
And then there are more LACs that people typically consider, but again that may or may not be something you would be interested in.