I am not building the layout, but have been following the progress. From a building point of view, the 1/4 will provide adequate backing for the foam and maintaining the frame square without the weight. Since it is relativly small and you will be able to reach all points of the layout, there would be no need to climb onto the layout or build it to support anything in excess of more than a few pounds per square foot. As far as holding screws the 1/2 would hold a screw with more gusto, but the 1/4 will hold enough for the purpose intended. Like all construction, there is always trade offs of cost, strength, weight, and what is needed and you balance them as you see fit.
Jim