I don't know if you've tried this, but I have had a lot of luck with
Take a leather mallet that is as close as possible to covering the
entire surface of the piece (if it's a bit larger, that's great).
Lay the piece on the anvil and the mallet on top of the piece. Use a
heavy-head brass hammer (or really any heavy-head hammer/mallet) and
hammer onto the leather mallet.
Basically, it's creating a "sandwich" between the leather mallet and
the anvil, and should work well to flatten the piece evenly. You're
not hammering directly on the piece, so the distortion won't affect
your ability to flatten it.
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