The next step was to add the magnets. I acquired 100 1/2"x1/2"x1/8" powerful rare-earth magnets for around $50 on ebay:
They were very difficult to separate from one another and by the end of the day, my right thumb was feeling quite numb but with some time and work, the magnets filled the channel cut by the router. Part of the effort was aligning the magnets so that they stuck to each other. If they were aligned properly, there was a danger that they would collide to violently. These magnets are so powerful that they can collide with each other destructively, leaving expensive magnet shards. I lost a couple in this manner but was thankfully left with enough to finish this project.
The result was as good as I had hoped for:
The only thing remaining is to cover those counter-sunk screw holes with little wood disks. Other than that, I am happy with the outcome.