A word of caution.
A couple of months back I drilled off the heads and punched out the remaining bodies of the several rivets holding the rear cross member to the frame on my '41. At this point I should mention that the crossmember had a 4" bow pulled into it. This was probably a result of being pulled out of the mud by some really big truck, tractor, or dozer. So when the last rivet on one side was driven out it SHOT all the way across the garage and put a very nice river shaped hole in my drywall.
Lesson here....The rivets do fill the hole and there is no room for movement when the parts being held together are pulled or pushed out of the original alignment. When the rivet lets go something is going to move very quickly.