Not all was lost, however. I did make some serious headway in creating a router jig.
So, the centerboard is has a foil shape, not unlike an aircraft wing. It's important to get the board as symmetrical as possible, and that's where the jig comes in. It's basically a little track to keep the router from doing its own thing, and to keep me from taking too much out of the wrong spot.
The one in the very front is the first one I attempted. I used some scrap plywood but grossly underestimate how flexible a slim piece of plywood can be. The second one was cut out of a 2x4, and may actually end up being the one I'll use, with a few modifications.
And second, I'd be sure that the router bit doesn't touch the inside of your track. I didn't think to consider that. Live and learn.
Productive, if a bit frustrating day. At least I'm one step closer.
Building a sailboat and need more information about router jigs for shaping a centerboard? Here you go!
Duckworths' Another Approach to Shaping Foils
Small Craft Advisor's Forum 'Scratch Built Foils'