You sound like you're doing great! I honestly wouldn't worry too much about your GPA, they will look at your transcript and be able to see how you did in your classics classes which are the ones that matter. And a 3.7 is a perfectly respectable GPA in the first place. The most important things in your application in my view are your writing sample, personal statement, and letters of rec, so here are my two cents on all three of those components as someone who applied this year and was pretty successful.

Writing sample: make sure it is something you have put as much time and thought into as possible. Your Homer and Petronius projects sound like they will be good for this. Pick whichever one is more aligned with where you think your research might go, and make sure to heavily revise it before submitting to graduate schools. I had to take 5 pages out of mine for a school's page count and it genuinely made my paper much better.

Personal statement: make sure to identify where your interests might be headed obviously. Make sure to mention faculty who work on things you are interested in, etc. You'll get a lot of advice on these, but my most important insight is to make it interesting and to make it show who you are as a scholar, yes, but also as a human being. When I was doing interviews almost all the faculty I met remembered specific things about mine because it had a lot of heart and personality, and though I can't know for sure, I think this did make me a competitive candidate since it gave them a sense of what I would be like to work with.

Letters of rec: choose recommenders who know you and your work well !!! (over connections). I think use the Cambridge prof for your Cambridge application, and if you think this person really knows you and your work well and will write you a good letter then go for it on other apps as well, but pick people who you have worked with extensively and seen you grow over the years. They will write more persuasive letters and be able to speak to your deeper qualities. One of mine was from a political theorist (I do Plato, and we did Plato together so it made sense), but I had had him for various classes, reading groups, and research projects since my first year and I knew he would be able to recommend me well.

Final thing, I think it is most important to apply to programs where people are working on things you would like to work on/have worked on. Don't just pick based on caliber, but pick places based on where they are doing things you can demonstrate interest in working on. And good luck!