I think you have a chance at any of these schools. Obviously, UMass Amherst as your affordable safety, but you might get in anywhere.
I don’t know about SAT prep, but my kid took a practice ACT and got in the low 30’s for it, which was still better than his PSAT-predicted SAT score. He then prepped himself for it, maybe a total of 60 hours over a few months, using the free, legally downloadable retired ACT’s that are in the public domain, findable on the internet, and also in their Official Guide (you can buy a cheap one a couple of years old, because they just republish mostly the same tests). Basically, whenever he had time, he’d take a section or two of an old test, under timed circumstances, grade it, and go back and re-teach himself the math he needed to, or reviewed the grammar concept, or became familiar with the necessary data interpretation skill, or learned how to pick the BEST, most obvious right answer, from the test maker’s viewpoint, for the reading comprehension section. He got a 36 (34 in math, 36 in everything else). Afterward, once he’d begun Calc BC, he said that if he’d already had Calc, he would have probably been able to get a 36 in math, too, because even though the test supposedly doesn’t require Calc, knowing Calc would have made it possible to do certain problems faster (there’s a LOT of time pressure in the math section). The science section, as you know, is not science - it’s data interpretation, and in that, practice using old tests definitely makes perfect. There is a review on Amazon for the Official Guide that tells you which books are best for reviewing for ACT, if you need them, but it doesn’t sound as if you need any of them - you just need to use practice tests to prep.
With a household income of 85K, you need to target private schools that are generous with financial aid. You’ve already got a very nice record, and if you can get a spectacular standardized test score, it could help to set you apart from the crowd, and maybe make it possible for you to get into a top school that’s generous with fin aid.
About the essay - get your school counselor to cover the sob story in his/her letter, saying, “This kid has managed through these very difficult circumstances to continue to achieve at a very high level.” That way, you’re not crying that they should have pity on you, but the committee hears the story. Meanwhile, you write your essay in a way that SHOWS, rather than TELLS the admission committee what you want to convey. My son made several attempts, all very different, none felt right, and finally, his father asked him, “What do you LOVE? What makes you happy?” Son replied that music, playing ping pong with his father and big brother, and his intended field of study - which wasn’t ping pong or music - were the things that made him happy. He then crafted an essay around these three elements, and the commonality of them, and the concept of work vs play, and the overlap/interchangeability of work/play. In the essay, it SHOWED, rather than told, how hard he had worked at music since 3rd grade. It SHOWED, rather than told, about his love for his family. It showed his budding interest in his intended field of study. We thought it was a pretty good essay. There was a serious sob story background, but he let the school counselor put that in her letter - never mentioned it in his essay, other than maybe tangentially.
You have good ECs, sounds as if your counselor could write you a great letter. Get to know the counselor who’s writing the cover letter. Make appointments to go talk with them, to ask for advice about where to apply for what you want. It’s not that you necessarily need that advice - it’s that you want the counselor to get to know you, and your sob story background, and your ambitions, and like you, and want to write you a great letter.
The one part of your application that is lacking is awards. It would be wonderful if you had some kind of regional, statewide, or better yet, national recognition of your talent or achievement, in any of your areas of interest - either academic or extracurricular. You say you write well - can you enter some competitions? I know that Covid has made in-person anything difficult, but there are some competitions/awards that don’t require in-person meets or competitions. You might want to start a separate thread for advice on what you might be able to enter, soon, so that you might have some kind of recognition/award to put on the application.
Best of luck. You sound like a great applicant, will do well wherever you go, even if it’s ‘only’ UMass Amherst, which is a great place - lucky for you that you have that in-state safety.