Whether or not you ask a need-aware holistic private for aid, if you don’t match, you won’t get far. It’s a big leap to assume needing aid is the only pitfall.
At this point, I’d suggest more attention to combing your app/supps to see if you do match. It’s more than stats and some ECs. Do you know the college well enough? Can you properly answer any Why Us (which can also be behind some/all supp questions.)
Learn how need aware works, how different colleges among your targets look at need and when. Many explain on their web sites.
A need-aware can have some early-ish convo with FA folks. They won’t wait til past the final decisions, all the work involved. Need aware for decisions implies “need informed” during reviews. There can be different ways these school do that. Or how they code the level of need.