Getting 3D Meshes to render with UI according to heirarchy

Where we have Unity UI objects we're able to re-arrange them according to hierarchy position, the further down the hierarchy that a UI object it - the further forward it renders.

Now - I want to add a 3D mesh into this mix where the 3D object has UI elements both in-front and behind, the 3D mesh would also render at the appropriate time according to its position in the hierarchy.

Now, I've ruled out using multiple cameras because this may happen in numerous places so it's a pretty verbose solution.

I've similarly ruled out using the Z position because I need to use a perspective camera and changing the Z of UI / 3D meshes has an impact upon their size / pespective.

So my question is, am I able to do this through shaders? Is it possible to use a custom shader to force a 3D mesh to be a part of that UI queue?

Any help would be much appreciated!