So once I got home, I cleared the bikes and car from the garage, got Perry's help to put a 9mm sheet on the bench, and marked out the spine on it. Then I cut that out with a jigsaw, and repeated the exercise twice to make doublers for the front section. Then I clamped the three bits of ply together and worked them with my trim router (think tiny cuts) and sandpaper in a block until I was happy with the curves, and all three pieces matched nicely.
Here's what I'm trying to make, from my model. The spine is a good spot to start, because it's a manageable size, but a fair bit of the boat (bulkheads 1 through 3) hangs off it, so I can construct a largish subassembly that then gets attached to the rest of the boat before having to permanently banish the car from the garage:
Oh, and I've come up with a name for my boat. It'll be Elena.