Your clamp idea is worth trying. I have "fixed" this kind of damage a couple of times. Can be done. I have generally approached it with pliers/Vice-Grips, gently, slowly. Gentle tapping can be used, also. Some like to heat the metal with a torch; it does help, I imagine, but I have not tried it.
If it breaks, brass and epoxy become your best route; add a brass shelf and "rebuild" the broken area.
Don't expect perfection - I am sure that you do not - as it is essentially impossible and sometimes that "just one more tap/squeeze..." can be one too many. You are going to have to address the surface scars anyway, with epoxy or filler and files or some such.
