Going back to the 1944 Gun Digest, in its catalog section (which really represented S&W's pre-WWII offerings), "Checkering," not "Checking," is used throughout. As is "Stocks."

"As far as the yoke/crane usage, I have often wondered if the boys chose that term just to be different than their largest competitor from Connecticut."

Very possibly so, as Colt came out with hand ejectors having "cranes" before S&W did.