Congrats on your excellent acceptances. It sounds like you are being thoughtful about your choices and starting to eliminate some which is a good first step.
Any of these schools will allow you to achieve your goals, and the BME curriculum is ABET accredited at all the US schools you are considering.
If you think that Tulane is a good fit, you should seriously consider it. It is a very different vibe than GTech. Both USC and Tulane are more social, more work hard play hard.
I disagree with those who are slamming Tulane’s admissions practices…Tulane BME is the real deal, again it’s ABET accredited and the curriculum rigorous.
Who cares what the admissions practices are, or that they have implemented strategies to increase their USNWR ranking? You will never have contact with admissions once you are on campus. Yes, Tulane fills much of it’s class in EDI/II and aggressively markets, but they are relatively more transparent about their admission practices than many schools.
Regarding walking on for your sport, that will be relatively more difficult at Div 1 schools (Tulane, Ga Tech, USC), than D3 schools like Case. Sounds like you have spoken with some coaches, which is exactly what you have to do.
Good luck as you make your choice, keep us updated!
ETA: I agree USC is not worth the extra money. Not sure if Purdue is still in the running, but do note that you will do FYE (the first year general engineering program) and then transfer to your desired major. BME is competitive, although most students do get their choice of major if they satisfy the entry criteria…so research that if Purdue is still in the mix. Transition to Major - School of Engineering Education - Purdue University
Why is this relevant to OP’s decision of where to attend? And yes, Tulane does have two supplemental essays, 800 words max. They label them as optional, but they aren’t…the vast majority of students accepted completed these and did a great job on them (Tulane provides a great deal of direction on what they are looking for in the essays, unlike some schools).