I have not delved into the math of Developable surfaces for awhile, but I can say from practical experience that the bottom panel of a S&G kayak can be tricky.

My take on it is: Developable surfaces assume a panel that is 4 edges on a kayak this translates to: Chine, Keel, Bow and Stern Stems. But in reality the Keel and two stems are continuous, often with fair curvature from the keel to the stem, so the surface has two edges and translating the 4 edges of the developable surface to 2 creates more twist.

For the Developable surface with 4 edges the stems must be straight, otherwise it can't develop. But this will create a kink in the plywood at the base of the stem adjacent to the keel. To make this in plywood you need to cut off the corner between the keel and the stem, rounding out the stems and creating a smooth transition between keel and stem.

I have found that whether a strictly developable ruling exists or not depends on the transition from keel to stems. I add the stems to the keel. Generally, Bezier curves with c2 continuity are much better than if there is a discontinuity in the curvature, but this also applies to the chines and sheer line. Fair curves seem to be easier for finding rulings.

If I omit the stems and simply look for rulings between chine and keel, I get two cones that are at the end points of the keel and the stems are then given by the edge ruling lines and like you said, they must be straight lines. If the keel has no rocker, then the third cone tip has to be somewhere on the chine. It is this limit case where there are exactly three conic sections with cone tips that lie on the curves themselves that makes me think the ruling lines for bottom panels must all be of similar nature, as any possible changes in geometry, such as adding more rocker, are fairly small compared to the length of the kayak.

Using NURBS surfaces I've dealt with this in two ways, instead of being 1st degree NURBS in the Keel-to-Chine direction, I will use 2nd or 3rd order surfaces and fake a developable surface, i.e make a surface that maybe developed even if it is not strictly Developable.

Another way is to run the surfaces past the centerline and trim it back to the centerline. This can allow you to create a surface that is developable but only use part of it to create the desired shape.

I imagine extending the surface past the centerline would make it easier to find the developable surface, but one would lose control over the exact shape of the stem, as it would be given by the intersection of the surface with a plane.

I don't have that capability, my code is very simple and does not really deal with surfaces explicitly. I only model the chines and keel as cubic Bezier curves. The surface model is given by cross sections that have straight lines connecting points with the same longitudinal coordinate on keel, chine and sheer, like an SOF design. Curiously, the commercial S&G designs for which line drawings are available on the web all seem to show straight line connections in the body plan, but it is sometimes hard to tell. Either the designs are developed using almost vertical rulings, or the cross sections do not accurately reflect the developed shape.

upchurchmr's suggestion of the BoatDesign forums is a good one, there may be participant there who have dealt more with the math, instead of just finding techniques to hack what is available into a solution that can be built.

That forum has come up in my search as well. I thought the kayak forum would be a better place, as the issue is pretty specific to the shape of the bottom panel on kayaks and I read this forum anyway. I do enjoy the math and numerical methods, but ultimately, I am interested in finding a technique to hack a solution into something that can be built, as you put it. I have some work to do on the design before I start building a model, but I am looking for suggestions for materials to use for model building at 1:8 scale or so. Something that would be just as difficult to bend at the small scale as 4mm marine ply at full scale. Any suggestions would be appreciated.