Well done, AldenPyle! A suggestion...So that's the thesis. The natural shoulder style was a counter-reaction to the foreign elements introduced in the 1930's; keeping the good parts and returning to the traditional American style. This change was centered at Yale probably due to the sack suit loyalty of J. Press. The "Ivy League look" was a radical codification of that counter-reaction.
I think it's possible, even probable, that the credit you give to J. Press belongs to Langrock instead. Langrock (est. 1898) predates J. Press by a mere four years, but it successfully promoted the "new" sack suit look from the get-go. Furthermore, Langrock was then considered more upper crust --and therefore more desirable (and influential?)-- than J. Press. For starters, Jacopi Press was Jewish; David Langrock was not. In less enlightened times, such a fact mattered to trendsetting bluebloods.
J. Press then did what it had to do: it copied Langrock's merchandise styles. Time passed, the student body grew more diverse, and J. Press began to seem more attractive. Langrock tried to hold its place on Mount Olympus, but never became iconic beyond its declining circle of patrons. Meanwhile, J. Press became a byword for the Ivy look. Such is retail.