A design change
A little while back I built an octave mandolin. I built what is called a ‘flat top’ mandolin (as opposed to a carved top like a violin) though the top and back are not flat. Both the top and the back have a 15 foot radius. I have 15′ radius dishes from building ukuleles (the backs) so I was familiar with the radius of the plates.
I merged a couple of different plans, and settled on an X braced top. (I build ukuleles with X braced tops.) The plans also had an X braced back, so I did an X brace on the back as well.
On the next set of ukulele builds (tenors) I decided to try an X braced back with a single cross brace in the upper bout. It worked out really well. I think that the X holds the radius dome of the back better than the previously used 3 cross braces. I radiused the braces individually, glued the X together, and then re-sanded the entire X in the radius dish. With the X I could place the center of the dome exactly where I wanted it, and I was not relying on the radius profile of the sides to establish the top-to-bottom radius to match the side-to-side radius imparted by cross braces.
I also think that an X braced back puts less strain on the instrument with humidity changes. With a cross brace the back wood is expanding/contracting across the length of the brace. But the brace does not get much longer/shorter with humidity changes since wood does not change much in length. This always has bothered me. The back wood is expanding/contracting and trying to break free of the brace. With an X brace the stress should be less because the X is at 45 degrees to the direction of wood movement so there should be less movement per-unit-length of the brace. The X brace is longer so the wood movement is spread out over a longer distance.
I see no reason to go back to cross braced backs, at least on tenor or baritone sized instruments.