Regarding the aforementioned edition of "Columbia, The Gem Of The Ocean" (written by David T. Shaw in 1843), it might be worth mentioning that America Sings had six theaters and four scenes as well as the two load and unload "scenes." Each segment (including load and unload) lasted five seconds shy of four minutes.
After waiting in line, patrons entered a theater and were seated. Ten seconds after the doors opened, "Columbia, The Gem Of The Ocean" (1:35) started playing as background music. Five seconds after it ended, the brief introductory load show started and ran for just over two minutes. At that point, the theater would rotate to the "Old West" set before rotating again after 3:55 had passed This pattern was repeated three more times until patrons arrived at the unload set. The brief "Goodbye, goes the weasel!" scene played out and the up-tempo exit music started and *ended* before the theater rotated back to load.
As the load set was not the same as the unload set (they were very similar but I believe a zoo flat was featured in unload to help the ride operators distinguish it from load), I am unsure how anyone might hear the unload music in the load theater as the tag music ended before rotation. I personally sat and waited for the music to end dozens of times before exiting the theater. (Ride operators still had about a minute to kick out any stragglers before rotation.)
However, I suppose it is possible that the track might have been re-stared during rotation as in early '81, the load version of "Columbia" was no longer utilized. I never heard the unload music in the first theater, though. After they stopped using "Columbia" there was no audio at all until the introductory show started.