Not the answer you are looking for, but I gave up trying to use Photoshop for 3D, after finding how much easier it is with After Effects. Cory Barker and Planet Photoshop used to be the go to place for Photoshop 3D tutorials, but he spends all his time on Kelby TV nowadays. He is still the go to man for Photoshop 3D though, and there are hundreds of programs to search.
Split Extrusions only works for a Ps generated extrusion which by definition is generated on a single 3D layer. You can generate a multi-object extrusion, by merging shapes before extruding, or by extruding a multi-part selection. There's no need to separate the 3 split ojbects to separate layers, unless you don't want them rendering as a set.
1) CIrcle marquee select 3 times on the canvas with the shift key held down.
2) 3D extrusion from current selection
3) make sure to select the extrusion mesh in the Scene panel and 3D> Split Extrusion
4) move each separate extrusion independently
Here's an example using rectangle shapes.