I built my own router table to mill the strips. It worked okay, but not great. No combination of feather boards seemed to hold the strips in alignment consistently. As a result, the boards wandered just enough so that the beads and coves weren't perfectly aligned throughout the lengths of the strips. It worked out; I used the strips, the kayak is built, and it's okay. However, I had to do a lot more sanding and planing once the shell was complete, in order to get out all the little grooves between strips where they didn't quite line up. As a result, the boat is probably a little thinner than 1/4" in lots of places.

In hindsight, I think I should have taken Nick's suggestion from the book: build a simple table with a 3/4" plywood top, bore a hole the slightest bit bigger than the diameter of the router bit, and screw the router to the underside, either by drilling holes in the router base, or using washers to hold the edges. I think the problem with my setup was that the hole that the bits came through was too large and the strips bent down sometimes when they were passing through.

Another thing I would like to do next time: rip all of the strips proud of 1/4" thick, then plane them down to 1/4" with a surface planer. I ripped the strips on my table saw to the best of my ability, but they still weren't all of uniform thickness.