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That sounds like it might be the way to go.
Again with the motorbike refrencing... but they often use sandbags to help limit the movement on the back as they hit the metal, and allow the metal to stretch with the blow and make a smaller, more controlled bends/curves.

Not necessarily saying buy a specialist sandbag, but again thinking about the principle - if you can put something solid with some give behind it or make your own temporary mini sandbag - then it should help reduce deformation.
I think.
hugo7
kvragu
If I'm understanding you, are you saying hold the curve stable with some fixing while denting the sides? That would make sense but I don't think I have something like that available.
Maybe hammering the sides rather than bending? That might distort the material more locally?