Hey Jerry,
You can attach a 3D texture or 2D array texture layer to a FBO with 'framebufferTextureLayer', see [1].
Unfortunately you can't bind a whole 3D texture like you can in desktop GL. This is because we don't have access to geometry shaders, which can pick a layer to render into after the vertex shader stage.
I was thinking about this restriction for my own project, and the idea I was considering was to use MRT. One color attachment matches one z plane, and condense your solve into a sequence of draw calls. This at least cuts down on the number of draw calls by a factor of 'MaxDrawBuffers'. There may be other solutions as well, maybe others have alternate suggestions.