I think of Furman’s closest academic peers being LACs like, say Sewanee, Rhodes, or Centre College. You don’t necessarily have to see it this way, nor order your preferences this way even if you do, but I would put Richmond and Washington and Lee into a different academic peer group, and then Davidson another still.
Comparing LACs and research universities is always problematic, but I’d say the closest to an academic peer on your list is probably Wake. The rest I would see as more equivalent to one of the other LACs you mentioned (exactly which depending on the university).
I note William & Mary is also a bit of an odd duck (in a good way for some kids). I’m not sure I would really be inclined to strongly associate it with any of those other schools. Honestly to me it sort of feels like a university equivalent of like a Macalester or Kenyon or such, and university-wise I tend to think of it as sorta like Tufts.