If those are 1/4" or 6.35mm audio phone jacks, I'm sure there are lots of electrical engineers who could design a pre-recorded player that would fit ENTIRELY inside the jack without protruding outside the jack whatsoever.

Eh, only one way to find out.

An ESP32-PICO-D4 is 7mm wide, but based on internal images it appears you can safely grind it down to ~6.35mm. It contains a DAC, 4MB flash, and all needed peripherals plus bluetooth. The quality [1] would be poor, but this matches what we observed.

A circuit board would probably be out of the question given the size. Even 0.8mm would have very little usable area. Flex PCB could work well, but is probably overkill for the complexity required. I'd expect a project like this to be hand soldered, given the low (less than 6?) component count. It wouldn't be easy, but well within the capabilities of a hobbyist at home with a cheap USB microscope.

For power, I could imagine a repurposed AirPod battery (they fit in the 0.235 inch diameter "stem" of the headphone) with a deadbugged switching or linear regulator fitting both the power budget and the size constraint.

From a physical design perspective, a lot of traditional methods seem impractical. With this size constraint one possibility could be placing requisite components into a 1/4" jack shaped mold, and casting it in epoxy in a vacuum, completing the conductive surfaces with copper tape.

1. https://www.youtube.com/watch?v=lgDu88Y411o

I could definitely make one as a demo.

The only problem, though, is then there need to be dozens of these because that airpod batter lasts maybe what, 2 flights?

Could that pick up a transmission from a device designed to emit RF stored in the overhead above?

Just put some beige box around it to make it look like it's part of the panel. The crew won't notice it.