If you go for the three row idea like I suggested, here are some ideas for longevity of use.
You want the 14 bead row where they are the easiest to get to since they will be used most of the time.
Plus, as I was thinking about all of this, string and even wire will give after a while, I wonder is you can use metal or wooden rods instead. I was thinking of old abacus'. The really old ones didn't last long due to the wires and stings stretching over a long period of time. That is where the tiny wooden rods came in and then eventually they went to metal. In all reality this is an abacus of sorts. It just has a specific purpose.
Regardless what you come up with, I do want 1 maybe even 2.