Greetings Clayton welcome to the Forum.
Some/many times, fans and Cages have a Balance Clip stuck on them, for Balancing.
It could be that it has come off, and seemingly be in good shape (no looseness) and the vibration occurs when the fan speeds up.
As far as accessing the Unit, look for any removable panels which would give you access to the area.
I have used Silicone Sealer on joints where metal touch another piece, sorta glues them together a little better, and dampens any vibration to some extent.
Have a good Day !
S.W.