Here is a post on Will Traux's blog about the rapid transition from the use of Scribe to Square Rule in Timber Framing. (He explains what those different rules mean.) The comments are an important part of the discussion.
I have also seen the rapid change from one system to the other starting around 1820.
I thought this could partially explain why accurate carpenter squares became so popular after 1820, why so many mills sprung up along Paran Creek in North Bennington and Shaftsbury, Vermont, to manufacture the squares, why after being wiped out by the disastrous flood in 1852, the factories were quickly rebuilt.
The comments to the original post discuss the need for standardized dimensions when using the Square Rule system. I think they make a good argument that standard measurements were not essential.
So I haven't a answer, yet.