Removing old warped solid rivets from transom

[willbennett00]

I am attempting to replace leaking rivets and likely the whole wood transom in my 1648. The solid rivets look like the previous owner attempted to rebuck the rivets but bent them in the center. I was able to punch a couple out after drilling the head off but they come out looking like a loose C shape. On the others I have tried on the transom they won’t budge at all when hit with the punch. I tried drilling further and just going through but that is proving to be difficult and time consuming.

Does anyone have any tips for removing extra stubborn solid rivets? I am assuming the wood is rotted and I worry it’s allowing the rivets to bend instead of come out.

Thanks for the help