Very cool. I like. Lot's of ideas coming to mind.
A round "radar" type screen
As you said, mirrors to scan across tube TV style (wonder what kind of resolution and refresh rate you could get?)
Steppers on an x/y for an Etch-a-sketch style toy
Wonder if you could make a makeshift UV laser by enclosing the UV LED(s) in a mirrored chamber with a single pinhole exit. Maybe a couple of lenses if it's flaring a bit.