I don't buy the idea that the falling shot is the five-inch miniature. A model that small would not seem to have either the mass or the mobility to bounce and flop like the one actually seen on screen. Sumbitch would bounce like a rubber ball. (Like the dorky little dummies in the spider-pit fall.)

I'd lean toward a full-sized dummy ape, with nobody but sawdust inside. Hypothetically you could shoot the fall on a white screen set-up from the right distance to get the full fall, then take that element and combine it with the fake Empire State Building. Clearly the building WAS a separate element-- matte painting, presumably-- since it's consistent in two separate types of trick shots, the animated climb upward, and the tumbling fall downward (however it was done).

Likewise the shot of Buzz Dixon (RKO's, not CHFB's) on a backlit miniature stage moving a puppet on a nondescript "building" with little pegs-- this clearly indicates this movement-element was printed into the panorama shot of the city, sandwiched between the background and laid over by the Empire State element to hide the "building" the puppet is climbing.

Given the way the animation cuts would have been composited, it's a relatively simple reprise of the same trick to add a falling-dummy element instead of the stop-motion climb.