Hi John, this is Matthew / Spike Glidden and hope I / we can cover the bases for you. :-)
I'm confident in the 1935 date for reasons that go beyond my SABR blog article, as Goudey's own card business got stuck in a rut by 1937, making it unlikely indeed that they would dust off a 1935 concept and throw it out into the market.
The basics of dating them remain straightforward, as the Knot Hole cards follow on the heels of Goudey's big launch of their Knot Hole League loyalty program featuring Lou Gehrig (1934) as a spokesman and the Knot Hole score cards feature pennant-winners from that 1934 season, Detroit and St. Louis. (As PSA itself notes, cards feature ©1935 in small type on each one.) These baseball flipping score cards follow a similar football set (Varsity Football) they had already released to support Sport Kings in 1933-34.
I suspect Goudey believed their 1935 baseball cards would sell at a similar rate to 1933-34, which would lead to lots of Knot Hole League giveaways. Unfortunately, the Knot Hole League cards are an uninspiring design, so I bet kids realized they could get more interesting stuff from Diamond Stars Gum, since National Chicle was offering large photos as trade-in bonuses. I think this forced Goudey to compete with their own large images, which pushed Knot Hole League to the back burner and introduced the premiums we now call R309-2. They then expanded those premiums into a larger program for 1936 with the R314 photos.
In addition to the 1930s business realities, there have been modern discoveries of somewhat narrow caches of 1934-35 cards that include Knot Hole League, implying those were available before 1937. While the card details and business realities of 1935 are more meaningful to me, that adds support to 1935 as the correct release date, at least in some markets.
There's an excellent chance Goudey was still giving out Knot Hole Cards in 1937 (and after), since they were rumored to have at least some extra stock of old releases well into the 40s. While I trust that PSA had reasons for setting 1937 as its date, it's such a modest set, there's no axe to grind on my side. For context, I think you could still get mid-1930s Goudey cards in "new" packs late that decade, due to massive overprinting during their 1933-34 boom years. (That's one reason Goudey might've printed their 1938 baseball cards as numeric extensions of the 1933 release.)
In short, a lot of things support 1935 as Knot Hole League's original release. If PSA was able to show their own work, I bet we could resolve any differences. Fortunately, no question about "true rookie cards" hang in the balance!
I wrote more about Knot Hole League as part of Goudey's overall business situation here:
https://www.number5typecollection.co...le-league.html
Off-the-cuff, I can easily believe Goudey continued to sell "1936 baseball" (the black-and-white flipping cards, which were undated and don't even say "Goudey" on them) well into 1937, given declining sales in 1935, and that this early shipment included a number of leftover Knot Hole League cards as in-store giveaways. This could lead one to call them a 1937 release, should that be the first time those cards arrived in that market.
Let me know if you have follow-up questions!