What an interesting challenge!
One possibility for an easy-to-repair nose might be to use magnets...maybe
hidden underneath the surfaces to be joined. Or make one surface metal, and
the other magnet. You could use magnetic sheets, perhaps, cut to size. A
thin paper cover that matches the rest of the bust could perhaps camouflage
the magnet. You'd have to make sure that they (the magnets on each surface,
if you magnetize the nose and the nose-spot) align correctly, or else the
nose will never attach in the right position.
Just a thought....
Amy in TN