I had the same question for my language assignment, and I'm pretty sure that it's "middle fiddle."
Yes, the noun 'game' does rhyme with the adjective 'game'. And the adjective 'game' does rhyme with the verb 'game'.
cherry ferry
cherry ferry
brief grief
limber timber
cool pool
roast toast
That would be the snake's flakes. A possessive noun-noun combination.
Cherry Ferry
loose caboose
You actually have and adjective (little) and a noun (stable), however, an alternate phrase could be a small barn.
blue canoe, cherry ferry