How to preserve parenting with one rig and multiple meshes?

Howdy!

I have a character rigged up in blender. I have one main mesh that is the body, and a few separate ones that are his eyes, eyelids, and whiskers. In blender, everyone sticks together, as I have the eye parts parented to the bones in the face. T pose and a pose from an animation in the pics.

When I import into unity however, the face parts are all spread around him. I've tried every combination of "apply transforms" I can think of in Blender. Not to say that couldn't be the issue, but I have certainly explored it.

I'm going about it this way because I want to use animation rigging to point his pupils places, and spring bones to have his tail and whiskers flop around. If there's a way better way for me to do this, I'm definitely all open to it! Weight painting all as one mesh isn't super appealing, and wouldn't work for the pupils anyway. Is it possible to have one rig control separate meshes in this way?