Mike,
Looking at your mock up of your cage I would highly suggest that you move the lower vertical bar that intercepts the angled door bar to be directly below the upper roll bar. It is all about load path. If you subject the upper bar to a high vertical down load ( read crash) the upper bar will have to bend, or shear, the angle door bar before the lower bar can transmit the load to the frame, could be down on your head by that time! My preference would be to both have the lower bar directly below the upper bar and also add a diagonal going back to the main roll bar at the bottom. See attached pics.
Rex