Why not make a die that complements the square punch? Just
the square punch and die are those you see around, I think I got
mine at Rio or DRS. When you insert the punch into the die without
any metal it is indeed a perfect fit, corners seat completely. But
when you've got metal in between there is a larger distance between
the relative corners of the punch and die than there is on the flats.
Draw two concentric squares, measure the separation along the flats
and then at the corners. The corner has a wider gap.
I don't know how one would make a better complimenting punch. If you
flared out the corners, that would probably make your finished object
significantly thinner at the corners and hammering the punch might
tend to chisel thru the metal.
I do enjoy a mechanical challenge though.