I found settings that allow the solution to converge. The changes I made were:

  1. change contact to Rough, which means no sliding
  2. change the contact Normal Stiffness back to the default value of 1
  3. turn on Weak Springs to resolve the rigid body motion issue
  4. suppress Remote Displacements
  5. reduce the pressure to 1e-5 MPa

This pressure will not push the corners down, so make the analysis a 2-step solution where a higher pressure can be applied in step 2.