You need to be applying primarily to test-optional schools, and choosing ones that either have a high acceptance rate, or have a median GPA below yours.
Your three test-optional schools are Goucher, Ursinus, and Denison
Goucher meets these criteria, with a median GPA of 3.15 - this is a great target.
Ursinus is good too, with a median GPA of 3.19
Denison’s median GPA is 3.6, and they accept less than 50%, so this is a reach. (Applying Early Decision would improve your chances, since the ED acceptance rate is 88%)
Marietta isn’t test-optional, but their averages aren’t that far above your stats, and their acceptance rate is high at 72%, so your chances there are decent.
At Miami of OH, your stats are below median but their admit rate is 65%, so you have a chance - probably 50:50 The Early Decision acceptance rate is 80%, so that would improve your chances.
I know you like College of Wooster. But realistically, it isn’t test-optional, and both your SAT and your GPA are way below their average. You really should apply Early Decision here if you want any reasonable chance of getting in. Without the advantage of ED I’d guess your chances would be 10% or less. The acceptance rate is 58% overall, but 77% early decision. Even ED I think your chances of getting in are probably 1 in 3 or less.
Beyond those… Bucknell, Carnegie Mellon, Haverford and Swarthmore really are not realistic at all. Their acceptance rates are too low for them to be admitting students way outside their normal stat ranges just because of nice essays or positive recs. Even if you were a recruited athlete and an under-represented minority, you probably wouldn’t get into these schools with your stats. Fortunately you have other really good options on your list.
In addition:
Look at UVA Wise. This is a match for your stats and has a high acceptance rate. And if you did really well there you might even be able to transfer to UVA Charlottesville.
Consider Radford University in Virginia. It’s not religiously affiliated, it’s test-optional and a good match for your GPA, and it has a minor in Classical Humanities (with courses in Latin, classical mythology, etc.).
And I’ve suggested Kalamazoo College before. Also no religious affiliation, test-optional, and has a full-blown Classics department just like Wooster does. http://reason.kzoo.edu/classics/ Your GPA is below their median, but they accept 72% of applicants, and they might be interested in an applicant who expressed a strong interest in their Classics department. Plus, their “K-plan” is very individualized, with lots of advising and support, and an open curriculum to focus on the subjects you care about. K-college is a worthy low-reach school for you. It offers both Early Decision and Early Action, and both improve your chances of getting in, over applying RD.
My suggestion:
Pick one school to apply to Early Decision:
Wooster, Denison, Miami of Ohio, Kalamazoo, Goucher, or Ursinus
(Wooster and Denison are riskier, but go for it of one of them is your true first choice. Miami-OH and Kalamazoo are good, realistic ED reaches. Goucher and Ursinus you’d probably get in anyway without ED as long as there’s nothing really negative/concerning in your application.)
Also apply Early Action to all of these besides your ED school:
Goucher, Ursinus, Miami of OH, Marietta;
and Kalamazoo, UVA Wise, and Radford if you decide to apply to those
(This way you should have at least a couple of acceptance offers before the holidays.)
If you don’t get into your ED school:
apply either ED2 or RD to Denison (if it wasn’t your ED1 school)
and apply RD to Miami of OH (if it wasn’t your ED1 school).
Good luck. Write a good, positive essay that isn’t about your mental health struggles - let your therapist address that part. Have a few people read what you’ve written and make suggestions. Show interest in all of your schools - visit if you can, and at least contact admissions and ask about remote interviews if you can’t.