I am probably getting in over my head by venturing to offer information about the ADKs, but I cannot suppress my google finger.
According to
this fiction piece by Joyce Carol Oates from Harper's Magazine, "They pronounced the name differently: Mitchell, O Sable, three syllables; Otto, Oz'ble, one elided syllable, as locals pronounced it."
Ausable Press says that it is a not-for-profit independent literary press located on the East Branch of the Ausable River in the Adirondack Mountains of northern New York, and that the pronunciation "aw-say'-bul".
This story by W. Mackay Laffan, published in 1878 in Scribner's Monthly, says "AuSable (pronounced up here Sawble, the Au, too being generally dropped)" -- but it refers to a Michigan river.
Fourpeaks' article "The Famous Swimming Holes In Jay, NY" mentions that the Bouquet River is pronounced boh-KWET or boh-KET.
This narrative mentions "Tahawus. ( pronounced locally as Ta-Haws, they drop the U )".
Looks like (as always) there's no clear answer, but Mavs's choices may be the "local" pronunciations. Isn't he a local anyhow?