According to this news video from Bowling Green ABC affiliate WBKO, the museum is working with geologists from Western Kentucky University and a recovery team to save the cars. An opening is being cut into the side of the Skydome (where the sinkhole developed) to insert a crane, and holes are also being cut into the floor to fill with concrete in an attempt to stabilize what's left of the weakened floor.
When the crane arrives, the extraction team plans to remove the cars' wheels and attach the cars directly to the crane's straps in order to provide a more secure connection than other methods. The team hopes to have all of the cars removed in the next two weeks.
After the cars are removed, GM has promised to oversee their restoration in-house at its Mechanical Assembly facility, which restores all of the GM Heritage Collection vehicles. Scroll down to get an in-depth scoop on how the Corvettes will be removed.