The Bumfortable isn't just for racing - it is also good for Sea Kayaks that don't have a seat that is an integral part of the kayak's structural support, or seal for a compartment for water tightness. Many people use the Bumfortable for recreational and touring boats.
Bumfortables require the supporting structure of a hull for its "shape", but not for "strength". It doesn't need lots of support, water is very supportive over the area of the seat. The skin of such a kayak structure provides the shape and support, but might deform the flow lines of the skin a little bit.
Plywood as a base and sides for the Bumfortable would also work, but I'd recommend making it thin and flexible plywood, or plastic sheeting. Using thick and rigid plywood is a heavier than necessary way to do it, and the rigidity of the plywood introduces a kind of "stress concentration" compared to the relative springiness of the rest of the frame.
If your kayak is wider than 500mm at the cockpit, you'll need a wedge kit of some other system to "fill the gap" between the Bumfortable and the sides of the hull.
One way to do this is to build your plywood sides close to the Bumfortable. Otherwise, get a wedge kit to fill the gap.
Another way to do it is to "hang" the Bumfortable in a kind of skin cradle, suspended from the coaming, with foam wedges on the sides to stop swinging side to side.