There is nothing about Furman’s Greek life that makes me think it wouldn’t be a good fit for the OP. It is a different system than you find at many schools, particularly in the South. None of the fraternities or sororities have houses on campus (sororities don’t have houses at all) and the parties are not on campus. The students live on campus all 4 years so everyone, regardless of Greek affiliation, eats and lives together on a daily basis. Recruitment is not cut-throat.
Furman has a strong record of med school acceptance and meets all of the OP’s wish list. I think it should stay on the list of schools to consider.
“- Overall: Well, what I guess I’m looking for is a diverse, friendly, smart student body at a school that is not overly competitive, cutthroat, or exceedingly difficult to get good grades in.”
I see that U Tulsa has already been mentioned and I want to second that motion. My S is enrolled there and of his 5 suitemates, two are from Canada and one from Ireland. His lab partners are from Malaysia! It has been a great experience for him. With 3500 graduates, Tulsa is large enough to offer a myriad of organizations, sports, etc. without being so large that you get lost or overlooked, even with your personality that isn’t extremely outgoing. They are very generous with merit money. The student body is definitely strong academically, with an average incoming ACT of 29, but there are plenty of schools which are more rigorous.
Wishing you the best in your search!