So the Antigravity prank is actually story based not reputation based, yo can find the exact time here (Spoilers).
To prevent objects from moving, you could nail them down or use hooks to prevent them from going to far.
I have also seen people have this event while away from the base in 0.8 (Don't know if it still works in the 0.9 test build)
The only other advice I can offer is that there are cheats (including tools) that can freeze objects in-place, these are patreon only, so if you have the means and don't mind cheats, that could be an option.
Sorry I can't be more help.