Just to verify, are you trying to make the cabinet so that you can scale it on all 3 axis? - make it taller, deeper, wider?
The "groove" in the side walls is the "dado", right? So it seems like the side walls are set up correctly so that they don't get any thicker as you scale the cabient wider. But if you scale it to be deeper, then yes the dado stretches. So you will need to make the last few inches into their own component with a fixed dimension, then have the rest of the walls scale. So that way the dado will not stretch.
Does that make sense? If not, I can try to mock up a model based on your model a little later tonight. Its a good looking model!
Chris