I think of it as a crop of the middle. ie I think of a 35mm lens on a crop frame as a 35 mm lens with the outside cropped off.
That's the thing I don't think most people who 'use DX for the reach' realize. That you can get that same exact reach on an FX, using the same exact lens (as long as the lens can be used on FX), simply by doing a DX crop on your FX shots. You dont actually get more reach by using DX, you're just forced to pre-crop everything. That 'extra reach' is nothing that a batch crop couldn't do in post.
Now, since I have actually shot more crop frame than full frame, when I use an FX, I actually tend to visualize the crop frame shot, but with extra frame around the edges.