Is 'strength' or 'stiffness' the priority?
If the frame longerons need to resist the tension of the skin, reducing the stiffness will be a problem.

Softwoods like spruce and cedar are surprisingly stiff compared to woods like oak and ash (especially if weight is considered).

Remember that stiffness (resistance to deflection of a beam) varies with the cube of the depth, and directly with the width. Small changes in depth can have a big effect.

Probably the safest thing to do is to spend an evening with some wood strips and string and weights, and get some data with your red oak vs softwood.