Princeton has SCEA, and that’s an option I strongly recommend considering. OP would get a legacy bump, and Princeton is as generous with financial aid as it gets. Even if admitted, there’s no binding decision as in ED.
If @thrillburn2016 is rejected or deferred - not an uncommon outcome, even for good legacy applicants - that opens the door for RD applications at less selective universities, some of which (s)he may prefer.
If you have a nearly perfect GPA and high test scores (which you’d need for a good shot at Princeton/Penn), you would be a strong candidate for generous merit scholarships at many colleges…something for you and your parents to consider. Of the colleges you list, Tulane in particular has been pretty generous with merit scholarships.
You certainly don’t have to attend an Ivy to succeed. As just one example, Evil_Robot chose Vanderbilt over various elite colleges (Yale, Stanford, Berkeley EECS, etc.) a few years ago due to financial reasons and wound up doing rather well for himself.