The next step was the one which scared me the most - the binding. I had carefully cut a rebate of approximately 1mm on the top, but it was not enough. Granted, I was also using a too-small binding, one more commonly used for necks, but it's what I had and I wasn't about to wait months for the Post Office to deliver a new one from Stewmac!
First, I taped the binding to the inverse of the top and left it that way for a few days to stretch. Tight corners were done with a bit of elbow grease and a hair dryer.
The first rebate was not sufficient.
Fortunately, a local hero stepped up and helped me out. Sashien aka Chocklit_Thunda and his father have a mean workshop, and we quickly cut the rebate a bit deeper.
We then proceeded to slowly plane down the top until the thickness and weight were as close to perfect as someone with my lack of finesse is likely to get.