I had to carefully trim my cork gaskets down thinner with a good sharp razor knife and still fought to get them in.
Typical fit for most reproduction parts.
Man, ...you went about it the hard way!!Since you are in to the wood scene, just clamp both pieces in-between two pieces of wood and use some clamps to compress the cork. After 15 minutes or so, when you can remove it the cork will remain compressed for more than enough time for you to insert it in the channel.
won't it pop out down the road if you open the cover?