The back came from the same piece of maple as the neck and sides. I cut the stock into 5 inch wide boards, each about 5/16ths of an inch thick. This was a bit thicker than needed, but I didn't know how much planing would remove (and too thick is always better than too thin.) After planing to remove the rough bandsaw cut edge, the thickness was about 3/16ths thick.
Most important while jointing the back by hand (especially with a very short plane, a longer plane would make this much easier) was to not over do it. I started by taking the two ends down since they are waste and so they wouldn't interfere with the center section which needs to fit precisely. For the actual jointing, I started with the edges matched together as closely as possible. Then I ran the plane over the edges in a few smooth strokes, just to bring them flush and parallel to one another. This all that was needed to get a near invisible joint.
Glueing the Center Joint
To put even tension on the joint, I secured long wooden braces on either side of the back a little closer together than necessary for the back to fit so that the back would tee-pee. With the clamps secured and glue added to the joint, I collapsed the tee-pee and added a clamp down the center to hold everything flat.
Glueing on the Bracing
I used the rim again to trace the back pattern. The lateral braces were secured in the same way as with the top bracing.
I didn't join the lateral braces to the center support. Instead, the center support is made from three different pieces. Very soon after I attached the bracing, the back quickly bowed. I'm still not sure why this happened. It wasn't so much of a problem that I couldn't fit the back to the rim, but it was annoying. It happened again on my second mandolin (a similar design), so I removed the cross braces leaving only the vertical center brace (which is one piece on that mandolin.) I doubt the lack of lateral bracing will hurt the sound, and I know it is still plenty strong. I am definetely just going leave the cross braces off my next flat top entirely.
Here is the custom label. It really feels like the thing is coming together when the label goes in even though it is just paper.
The completed back ready for assembly...