"And these kinds of musicians generally behaved as if 12-bar and 16-bar songs were equally authentically 'blues,' and often switched between 12-bar and 16-bar in the same tune."

Getting back to what jazz musicians apparently would have heard a lot of in New Orleans in about 1911 if they had been terribly interested in folk blues as of about 1911, here's are some examples of musicians who mixed 12-bar with 16-bar as if both were authentically blues and it made little difference which you did:

Peg Leg Howell (23 years old in 1911) "Fo' Day Blues"
Leadbelly (about 23 years old in 1911) "Blues I Got Make A New-Born Baby Cry"
Roy Harvey (about 19 years old in 1911) "Steamboat Man"
Jimmie Tarlton (about 19 years old in 1911) "Put-Together Blues"
Elizabeth Cotten (about 18 years old in 1911) "Vastopol"
Bo Carter (about 17 years old in 1911) "Pussy Cat Blues" (the 1931 recording)
Smith Casey (about 16 years old in 1911) "Santa Fe Blues"
Mance Lipscomb (about 16 years old in 1911) "Blues In G"
Reese Crenshaw (about 14 years old in 1911) "Trouble"
Furry Lewis (about 12 years old in 1911) "Mary Tell Blues"