That is a good idea! Well, originally I started out using all regular string, the loop was as well. I then switched to entirely fishing line which worked great as far as friction goes but the fishing line was pretty much impossible to work with for something like this which requires so much precision. Then I had the idea of using line only where I needed it, the loop, and everywhere else I used string. That is what I'm currently doing and it works nicely. The real friction issue I have now is just with the string and the cardboard as it goes through those holes, so I'm thinking of managing that by maybe lining the cardboard holes with plastic wrap or foil and maybe even oil it up a bit. The chicken wire is certainly a great idea, it would probably work a treat.
For now I'm going to put off my half adder until tomorrow maybe, but I'll likely record a video explaining the workings of the gate and such in a few minutes here.
Edit: Aye, I'm finding it quite tough to verbally explain how my logic gate works with the diagram, I suppose I'll let people continue to be in mystery until more ask how it works.