This was a result of poor investigation, lack of communication, and general stupidity. Of course the executors aren't supposed to run at level load, because they wouldn't know which player to affect. And if you check the NOCLIMB flag, which makes them affect all players, they work fine at level load.
Sorry about this mess, but at least I found a quirk amidst all this. The Change Music executor can only affect the player who triggers it.