You're assuming the strings were kept on the bows and that each bow had one string - dangerous!
I've always thought the "bowyer's" marks were actually draw weight identification. They're all so similar but for an extra mark it would make more sense. Three pricks, or 5 or 7 etc instead of lots of unique identifying symbols. Only a small amount have an actual symbol - a circle with a symbol inside it, for example - but the majority have a set of triangular pricks arranged in a certain shape, and I think the number of pricks correlates to the power of the bow. That would make the fact that each chest contained bows with different (but very similar) marks all the more reasonable. Otherwise you'd expect one bowyer's guild to complete a chest of bows, and ergo each chest would have a load of bows with the same bowyer's guild mark on them, which isn't the case at all.
It's almost impossible to confirm though, because we don't actually know the draw weights of them.
Oh, and if you make your arrows properly, and don't bind them with great thick linen like the reenactors do, and the bindings are seated in a traditional wax and resin compound you very rarely get any sort of wear mark from use.