The idea trying to be expressed, if I may and as I see it, is to put the 1/4 inch ply spars vertically butt glued between foam edges, so in a horizontal measurement along the length of the roof front to back that would be 2ft foam, 1/4 inch rib plywood, 2 ft foam, etc. The height of the narrow ply rib would match the thickness of the foam.
So you would glue the ply rib flat to the front or back edge of each piece of foam with the foam running across the width of the cabin.
One could even cut the ply rib spars with a little arch or crown, if you wanted to get fancy, but jigging up the joint gets a little more complicated. It could be done using a matching shaped caul and a clamp setup similar to the above, or how I glued my 1x2 and 2x2 roof spars to the top of my ceiling panel prior to install (would have to spend time looking for that in my build thread if anyone is still interested).
Laying the spars flat as backers, as shown in the ^ pic is much, much weaker, even if they are 3/4 pine (no offense intended, I just don't think you understood what was being suggested), but with added composite is probably also very strong.