True. I'm already thinking of the next one I want to build with some design changes.Neat idea!
Some triangles to back up the jaw holders would be easy enough...
Another thing you can do, if you haven't already sourced the tube, is just use a wider piece of tube for the body. If you go to, say, a 6"x4" tube, with the 6" laid horizontally you could get wider supper behind the jaws.....of course it'd also change the front and back plates and the base/mounting plate dimensions too.