Putting all the pieces together, I was able to create a GUI with a sprite layer, attach it to a camera with a texture buffer render target, and render the GUI onto a texture applied to a 3D surface. Then I used the picked UV coords to convert to mouse coordinates and send user events to the GUI. Here is the result:
This can be used for GUIs rendered onto surfaces in your game, or for a user interface that can be interacted with in VR. This example will be included in the next beta update.