Project Orion
We construct a dome of ablative material beneath the orbiter and light off a few nuclear bombs beneath it to get the old girl back in the air Project Orion style. Then we need Tom Cruise to land it in the new museum. The US has plenty of nukes laying around and we can tap the strategic circus peanut reserve to line the dome. The biggest expense will be product for Tom Cruise's hair. Things are only hard if you make them hard.
https://en.wikipedia.org/wiki/Project_Orion_(nuclear_propulsion)