Even in error, AA is sometimes useful by looking at their reference table.
On their first point (that the model numbers had an F prefix before 1937), they have an A-373 Supersocket booklet dated 10/30 which they say is the first time Williams drive tools appeared. They also have an A-373 Supersocket booklet dated 1/33 and a Tools of Industry catalog dated 2/33. Presumably, these are their source for the info. Unfortunately, they don't ever cite their sources in the narrative sections, so we can only assume that's what they used, and, they don't have an open source library, like TA had, so we can't check it for ourselves.
My info comes from the hardware store catalog I cited above, dated 1930. See Pic 1.
On their second point (that the speeder model number changed over to a B prefix in 1942), they have an A-409 Superrenches/Supersockets booklet dated 5/41 and another one dated 11/45. Note that they list nothing in between. Their next document is the 1947 Tools of Industry catalog. If they looked in the 11/45 A-409 and the speeder was B-15, I suppose they guessed that the change occurred sometime between the 5/41 A-409 and the 11/45 A-409.
They were wrong. As I said it is still F-15 in the 3/45 A-409. See Pic 2.
But that means it switched from F-15 to B-15 sometime between 3/45 and 11/45.
You have a really cool and unique set there, Otg. Still waiting to hear if anyone has ever seen another one, or any other Williams set in any other drive size with a diamond decal and the Williams drive size "pattern" nickname (i.e., "Midget", "Bantam," "Standard," "Heavy Duty" and "Extra Heavy Duty").