: or is there a method that I am not seeing right away?
not obvious, but will add a huge amt of stiffness right where you need it, is how you handle the bottom of the seat. in other words make the bottom of the seat say out of foam, stiff, flat and covering a large area.
at the front of the yak where there is large panel curvature for the bow upturn, you do not need any stiffening as the panel shape itself prevents oilcanning.

in the rear and feet area, make the chineseams radiused, use a few overglassed xbraces, or coremat, or doubled areas of 1/8ply. as the exterior triplanechines will be narrow (typical situation) no stiffening needed, so only add this doubling at some (say 1-2") distance in from the already stiff radiussed seam on only the central flat area.

the whole idea is to keep the wt down. you already have lots going for you to use for stiffness.

you could play around w/ foaming the inside for say 1/2-1" and glassing over that for big stiffness.

but the other real obvious simple boneass thing is to just add front and rear foam pillars and get going.