A lot of TOS items were simply tossed, (pun not intended) so it's a miracle the full size prop survived at all. The more recent photos show the restoration is coming along nicely.

This article about the Galileo's future home claims the restoration is already complete.

http://www.geekosystem.com/star-trek-shuttle-nasa-museum/

I wonder where the Galileo miniature shuttle is today? It was rescued, partially restored, and used in a TNG episode as set decor.

It would be so cool to own a authentic miniature, but how to take proper care of it? The larger Enterprise D model was showing some visible stress cracks when it was auctioned off. Even the SW models in Lucasfilm's care seem to be in rougher shape these days.