Is the origin of "butch" really from Polari?

I’ve been researching the origin of the term "butch" and noticed that sources tend to be split on whether they mention it originating from Polari.

OED, Green’s Dictionary of Slang (adj., noun) and the Online Etymology Dictionary all seem to point to entirely U.S. origins, presumably from a shortening of "butcher" to a stereotypically masculine nickname (~1870s), to a representation of masculinity generally (~1900s), to a gay male masculinity (~1930s), to a lesbian masculinity (~1940s).

Several sources (such as Fantabulosa: A Dictionary of Polari and Gay Slang) note that the term originates in Polari, a gay argot spoken primarily in England and Ireland (no time of origination is given, but late 19th or early 20th century is implied).

Did the term originate in the U.S., travel back to England, then travel back to the U.S. again?

Is there a crossing of potential etymologies here? Am I missing a primary resource or reference?

What is the presumed origination of "butch", taking into account Polari and non-Polari descriptions?