well its good that you thought about humidity, and I am taking it that the box corners will just be mitred… Wood expands approx. (depending on type of wood) 10% in direction of the grain 5%across the grain (from the center of the tree to out) and about .1% in the the end grain direction (so end grain of a board to other end grain), so the box itself will not move much at all and as long as the diagonal divider is not too thick (so that expansion will not push the miters apart, than expansion in the length direction should not be a problem at all. even with a large change in humidity,
The mitres should all stay together as long as you use a white PVC or PVA “D3” or D4 glue perhaps PU adheasive, and as long as you do not have extreme differences in grain direction from the side friese to the top friese and so on, so not a middle board and a extreme side board.
“Hoffman” keys or the bowtie shaped keys are always better than none. They give a large portion ofmechanical strength to the joint as well as more glue area. You could always try splines as well or perhaps a loose tounge on the inside of the joint. If you are also looking for something strong and quick a bisuit cutter machine is good too on mitres, depending on the machine of course (some may not adjust to cut in a 45 degree mitre angle)
Plywood in th back is great, you do not have to do any chiseling out in corners when you cut a grove with a mitre. A rabbit in the back may be even easier, because you can glue the box together and then just use some small planed out stock to hold it in from the back. The big advantage to this is that you do not have to have the plywood already finishd and makes sanding and finishing easier later, because you can do the back later or build it in later after the glue up is done, it is one less thing to worry about when glueing something. Sometimes its helpful sometimes not… it all depends on what you need, since you can not see the back as I assume it would hang on the wall, it does not necessarily have to be grooved in.
hope this is helpful
-- Nicholas, Journeyman Cabinetmaker, Partenkirchen, Germany