Something worth noting: one of the factors involved in credit-score calculation is the ratio of the average amount of credit you use to the average amount of available credit you have. The algorithms are of course quite secret (since they want to prevent people from gaming the system), but from what I understand it's good to try to keep your credit used at about a third of the total credit you have available. (I expect it's better if your ratio is too low than if it's too high, so in general an increase in your credit limit should probably help rather than hurt you.)

Based on the answers so far, I don't think I "answered my own question" at all.

@littleadv Sounds like the verdict is that the "fold and tear" system is cheaper, then, given a sufficient economy of scale (since presumably the machines to make them are fairly expensive).