Last '33 we did the compressed paper was 80% gone so we removed the rest of it, then drilled the rivets and removed the thin metal channel that held the paper. It was in good shape so we had it powder coated black, we then reinstalled the channel using pop rivets along with sealer between the channel and body. Once that was in place we put new plastic tack strip into the channel, holding it under the outer lip as it was narrower than the original paper. We also put sealer under it and secured it with more pop rivets. The wire, padding and topping was then installed as normal. Luckily the original top molding was complete and in good shape, so we had it powder coated and then installed as normal.
I've taken apart quite few '33-'34 tops and have never seen a trim clip like in rockfla's picture over where the ends butt up. Interesting to see that clip.