Jim,
There is a trick for making the two pieces of wood fit absolutely perfect that I have used many times for fitting a buttplate to a stock. I first learned this when fitting hooked buttplates with top extensions on muzzleloaders. They are a bugger to inlet and fit perfectly.
When you get the two pieces as flat and as close fitting as you can, get some two inch wide fairly coarse grit emery tape. It
comes on a roll. I use it a lot on the farm for cleaning up shafts before putting a new bearing back on it. Clamp the buttstock in a vise securely with the butt straight up and pull the strip of emery between the butt and the extension while putting firm pressure down on the extension with the other hand. You have to pick up the extension and reposition the emery each time, but in a while you will have a fit so close that it will look grown in place. The emery only cuts the high spots when you do this until the high spots are gone. You can judge when you've gone far enough. Cut top for awile, then flip the emery and cut bottom. Very easy and works great.
I'd like to try this, however wouldn't it be easy to round over the edge if you didn't pull completely straight out with the emery cloth?