So I spent some time and drew the projected dome in CAD software so I could get measurements and determine how much cloth to cover it.
The dome is ~13 feet high, and fits in a 10x10 booth area with a 6 foot wide door. Theoretically, the projector is inside, and projects the demo onto the surface of the egg for demos... or something. To be made of some sort of stretchy cloth.
Now to find suitable fire retardant stretchy cloth...