Benson might have some good information on this; my thoughts here are just speculation -- prior to the Fair Labor Standards Act of 1938, much work in many industries was done on a 'piece work" basis. Weaving canoe seats is the sort of task that would lend itself to being paid on a piece work basis.
Much "piece work" ended after 1938 because the average wages paid by piece work had to equal at least the minimum wage -- a new notion at the time. And piece work done at home by housewives, a practice used by many industries where the materials were supplied by the company to the home worker, was almost completely ended by the 1938 statute, because home piece work was often done sporadically, and it was not possible to correlate wages, hours worked, and pieces made. I don't know if Old Town or any other canoe companies had seats woven by women at home, but it is the sort of task that would lend itself to home work. And I expect that machine-woven cane came into use some time after 1938 because it would better lend itself to a non-piece-work factory setting than would hand-weaving.
In any event, it would not surprise me if the "canoe weave," and other weaving patterns which are simpler than the standard 7 step weave, were used, or even developed, by piece-workers who had a strong incentive to weave in a way that led to higher output per day.