Wow, compound curves are always a favorite subject of mine! I was able to keep the end caps on mine, but have thought about what I would have done, at idle moments...
First off, cutting the sections requires long curves, but I guess you have realized that. I would think about cutting out the majority of the endcap, leaving just a frame around the edge. With the frame mounted on the trailer, rough cut every other section. Attach these with Clecos, and use a big flexible ruler to lay out the lines. Take these down and cut them out. Repeat the process with the others, and use the sections that you cut out to mark the next batch.
I would use butt joints, and then put on a narrow trim strip between the sections. Your choice as to materials, as you can use a thin (1/8") bendy ply, and veneer on something very nice. I would be tempted to do some wild, but then that's me. I saw a pic of a Timeless trailer that used a hickory veneer, very patterned, that looked awesome!
Or go with hammered copper, or Lagoon Alabaster veneer like I did, for my table and end shelves... with wenge and aspen strips on the edges.