Well, that helped a little. I was able to search on 'rack' and find several activators. I was able to summon one to my position using placeatme, but activating them (even though they were invisible) wouldn't allow me to put my staff in them. It said I needed to have a weapon equipped to put it in the rack. Apparently the game doesn't consider staves to be weapons.

Does anyone know if there is something to place staves in for display? Any idea what it is called?

Glitch confirmed: If the staff is found before starting the quest (can be doubles of the staff located throughout Skyrim), it will have weight, and can not be removed from the player's inventory. The quest will not show an icon on the map and dialogue options are not available to return the staff to Enthir. To fix these issues, equip the staff/staffs to the character, and activate a weapon rack. An icon will then show to pick up the staff. Do this and the quest will update, stating to return the staff to Enthir.