I went through quite some amount of cedar for our first Kayak (Great Auk, right outa the book) and found that I had to be quite picky about colour and strip quality. Small seeming flaws jump out dramatically when it too damn late to fix em. When I routered the bead and cove I passed the strips between the fence and the cutter and cut with the rotation (Yeah I know, tremendously hazardous to the drywall). What I did do though in this process to mitigate this hazard was to use four separate featherboards, two on the infeed and two outfeed, whch served both to guide the strips through and hold them back from from becoming cedar arrows. What I got was perfectly cut beads and coves and no variations in width.
What has to be considered is that there really is very small amounts of cedar being removed from the strip as it passes through the cutters which means there isn't all that much tug on the wood. I had to push the wood through and tug out the last couple of feet.