Since you mention a router plane, I assume you may have one (as opposed to a plow, which I agree is the best choice, but one you may not want to buy for this project). Personally, I would try the router plane above a chisel or saw. Rig up a fence out of some scrap wood to keep the blade at the distance from the edge you want, and I think you will get pretty decent results. As with a plow, it would probably help to start the groove "at the end" and work back towards you.
I have used my router plane with one side in the air, but I think your idea of clamping a board next to it is probably a good one.