How did you end up doing the dice physics? From what I can tell it's 3D dice on a plane is that correct? When were working on our dice game we weren't familiar enough 3D to want to attempt it but it seemed like it had a lot of advantages.
I followed this tutorial for the dice and put some parts of the 3D world inside separate SubViewports. Rest of the game is all 2D, I faked 3D with this shader for the UI.