One visual re-skin later and now I love them. This does not fundamentally change much about them or their lore, but I think it "clicks" with me better now. Here are some images of Bugbears as they appear in my setting:
So here's how I described it to my players: they literally appear before you as they look in this photo. As in, they look like people in costumes. To be clear, they aren't people in costumes. But they look like it. Some of them have people hands, sometimes they have a mask for a face, but this is just how their bodies are. It's really unsettling. To explain it better, I told them, "they look like the sort of thing a child would draw to show you the monster they see go bump in the night, but real." That's what their lore says they are and I decided to go weirdly far with it. They are, at least partially, literally creatures of children's nightmares.
Maybe modify their stats to match the appearance a bit more (e.g. that one that has no arms but is just a big head, give that fucker a gnarly bite attack) and incorporate stuff like the bells on their belts, the strange implements they carry, etc. But also try to make every bugbear unique if you can. Have some more: