I bent 5 mm (3/16 inch) Okoume marine grade ply (5 equal plys with minimum voids) over a 13-1/2 inch radius (343 mm) for my ceiling skin. I had some minor splitting on the edges of the outside ply and a minor buckle about 8 inches long where there was an internal failure of some plys (i.e. the layers between the inner and outer plys must have cracked locally). This prompted me to apply a layer of 6 oz glass weave and epoxy over the outside as a stabilizing element to prevent further splitting, but in the end it worked out good, so it can be done.
I did wet the outer surface, and took my time over a few days gradually pulling it down the first time (I did a dry fit before removing to do the interior stain and finish, then bent it again). Another trick was to use wooden washers, squares about 1-1/2 inches on a side made from the same 5 mm ply, to keep the screws from pulling thru. Once fully installed and the glue had set I went back and pulled the washers out one at a time and ran the screws back in. This really helped keep the screws from blowing thru, especially given that I was putting the skin on and off a couple of times.
Another thing was putting the spars on the ceiling skin first then installing the assembly. This kept the skin from drooping in the middle, but then my build is a little unique, not unlike Fredrick's method, so my ceiling was kind of like a more traditional roof skin.
I wouldn't try it with cheap underlay luan, the kind with two very thin outer layers and a thick punky core for fear that it would snap open. There is a lot of energy being stored in this wooden spring! In fact, looking at my front 1x2 spars today, the ones ahead of the fan bay 2x2's, they are both bowed down in the middle a tad from the ceiling skin trying to flatten back out still.
Starting about
here in my build thread I had already assembled the ceiling skin and roof spars and was getting ready to form it over the front radius for the first time.