The assumption you’re making with your question, “how much will my story help me” is that it will help you, and you seem to be unable to accept that your assumption might not be true. Finishing high school in a year – or even two – won’t help you with college admissions. It’s not even a question of how much. The answer is not at all.
You do realize that some of us work at elite colleges, right? We aren’t just some random people on the internet. So you can listen to our advice, or not. Or listen only to the parts that support your choice. If you apply and are rejected your app will be kept on file, so you’ll have to have some substantial additions to have a different outcome later. But if you want to gamble on acceptance with your current record go right ahead.
I don’t believe you’d be online posting in an anonymous forum if your parents were truly willing to send you to Manhattan on your own at 16, and willing to pay $30k+/year for a ~500 sq ft studio apartment (plus utilities, food, and transportation), in addition to the ~$50k/year tuition. Why would they pay well over $100k/year for you to go live on your own in Manhattan when you have perfectly good schools in FL? Waiting just a year or two will likely save them nearly a quarter of a million dollars.
Why would they spend that kind of money when they don’t have to? If they were willing, and all of you were certain that you’re on target to be accepted, you’d just do it. So I have to think that either they aren’t as ready to drop ~a half a million dollars on your college education as you say they are or somebody in your house isn’t sure you’re ready. But go ahead and apply and see what happens.