Plan A would be to scrounge a couple of decent sized offcuts of Code 5 sheet lead from a roofer - that is the thicker stuff used for valleys and gutters which comes on rolls in 18" and 24" width.
I'd be inclined to screw it onto some 3/4" ply, although that may well still result in a loud thwack on impact.
Plan B would be to scrounge a couple of bucketfuls of offcuts, pick up a cheap old saucepan from a boot sale and cast your own lead ingot, which could be thicker than 2x code 5 but would be bl00dy heavy if it is any size at all.
IMHO a piece of 1/4" steel plate would be a much better idea all round!
Adrian