Jiggs, the one time I did a juice groove on a cutting board, I used my router table with stops attached to the fence on either side of the piece to limit how far I could cut in either direction. It was a pain doing it this way. It took a lot of figuring and experimenting to get stop blocks positioned to stop the cuts in the right places. (And I had to set them twice...once for the long sides of the cutting board and again for the short sides.) Also, I had to start the cuts by pushing the board down on top of the spinning router bit. Since I took light cuts, I had to do that maneuver multiple times.
I think either a template or a clamped-on straight edge (being careful to not cut too far) would be easier to deal with and get good results.