Is there some farmer's trick to remove those "cut this out" metal plugs
that's pressed into steel solvent cans for shipping WITHOUT deforming the
rest of the lip of the can?

I normally just stab with a flat screwdriver, but any attempt to pry the
thing out usually leaves a dent in the to top of the can. Stuff like
acrylic cement dries up real fast even with the cap screwed on good.