Trimming & Shaping the Linings

You could use a plane to trim the linings down to the rib edge, but it almost seems safer to use a chisel to get really close, then use the sandpaper adhered to glass to level and even out the entire top surface.

Now you can trim the bottom edge of the linings down with a knife and use some sandpaper to smooth it.

Here's an extremely childish doodle of various lining shapes people use. The first or second shapes (or something between them) are great, just fine. The others show cuts that remove extra "bulk." Some makers worry about that sort of thing.