Yes, most likely higher volume means higher power. This is particularly true for devices with limited power so that were therefore designed to conserve power to a reasonable extent. A portable MP3 player running on batteries would be such a device.
Most likely, the MP3 player has a class D audio amp chip in it to drive the headphones. This is the most efficient way available to produce a power audio output signal. These things can be quite efficient. For a perfect class D amp, all the input power would go to drive the output. The output power is the square of the output voltage divided by the load impedance. If the output voltage doubles, the output power goes up by a factor of 4.
In reality you won't see a factor of 4 power draw increase from the batteries when the output voltage is doubled because there are losses in the system and some fixed bias currents for various circuits. However, there should still be a significant effect.
Basis for my unfounded assumptions: I think the magneto is flooding the engine assembly with noise. It isn't dissipative, and there is no connection to a larger ground. Given the insulating nature of design, not even earthed when landed. It's just one side of a circuit with big spikes on it.
So:
Don't earth your battery powered modules to chassis. You know it makes it worse.
Float the modules, make Faraday cages for the electronics modules and use screened cables for your interconnects.
Use the outer screen to connect the Faraday cages.
Connect the screen at both ends. ( contrary to normal practice.)
Float the electronics from the Faraday cages. Currents from the magneto and other RF sources in the environment are not wanted. (you will pick up plenty of RF once you get airborne)
Lightweight Faraday cages can be made from plastic enclosures and much conductive screening spray. ( generally on the inside, where it doesn't get rubbed off)
Where possible use transformer isolated differential signals between modules. Single ended or ground referenced signals will be problematic.
Shared power supply will cause problems, assume the power supply is a noise source. Try at least common mode chokes at the boards.
In noisy mobile systems there isn't a convenient chassis or ground to bypass power line noise to.
Antenna feedthroughs are problematic.
Military solutions to this kind of problem involve screening the noise sources as well. ( see the comment about Fitted For Radio (FFR) vehicles).
Best Answer
Yes, power factor is a characteristic of a load and how close it is to being purely resistive (current and voltage in phase). Power factor correction is generally a feature of a load (a computer, lighting system, etc.) that helps bring that load's current and voltage into phase alignment.