At this point you have multiple chance threads, I expect you have had very good guidance and support from your private prep school and I have to believe you know the answer to your question. YES, you will be a viable candidate but NO Yale admission is not guaranteed for any unhooked applicant. That is all any responsible poster here can tell you. Applying EA may help a bit, but I have seen some truly outstanding candidates deferred in the EA round (some of whom were accepted in the RD round).
The very positive news is that you have done extraordinarily well in HS and if Yale doesn’t work out as hoped, then you should still have many many outstanding college choices. I’d recommend that you give up the idea of Yale as a dream school and work to create a solid college list that includes reach, match, and safety schools that appear affordable (find out your parents’ budget and run the net price calculator for each school) and that you would be excited to attend. The people I see who get hurt by the college admission process are the ones who focus on one or two hyper-competitive schools and then don’t get in. There are many wonderful schools out there where you can have a great 4 year experience and get wherever you want to go in life.
I would suggest is that instead of being “nervous and dilly dally on this thread despite knowing my rough answer” that you move on to more productive uses of your time.
Good luck.