The crust would basically switch places with the less dense lower layers. You’d have to bust out Archimedes’s buoyancy formula and figure out the values, but this would happen slow enough that it would be a period of incessant earthquakes, volcanic eruptions of magma, and great rifts. As more chunks broke lose and were pulled downward it would start to go very rapidly. So, maybe days of tectonic flux and cracking, then hours to minutes until the molten inner layers sit atop the old, now melting crust. The molten crust would now begin to harden into a new crust. Hopefully panspermic comets come by again.
Note: by doubling the density of the crust layer your respectively doubling the energy potential of the crust, so our planet would be hotter and behave like it did perhaps billions of years ago or more when it was first starting to form stable crust from magma.