I'm sure you have tried a lot of things that you didn't write up in your summary so apologies in advance if I'm suggesting something you have covered here.
It's kind of implied that the radio is still squelching correctly, and that you only hear this noise when a station is actively being received and triggering the squelch? If you disable squelch on the radio is the (offending) noise of a constant amplitude regardless of whether a strong signal is being received? I find the directionality you noted very hard to explain.
The change of antenna to a high gain on COM1 causing the noise to become louder indicates strongly that it's RFI coupled via the antenna rather than via power cabling/chassis etc. Does selction of different radio frequency affect the noise amplitude in any way? Noise generated from an engine source is likely to be relatively low frequency and coupling into the last stages of the radio electronics so it's likely unaffected by tuning but affected by audio controls such as volume. Does no antenna at all cause the noise not to be heard?
The fact that the frequency of the noise is completely unaffected by RPM really makes it not sound like classic alternator/magneto noise sources. I know you described the noise as "white noise", but is it really a pure random sounding hiss of wide audio frequency range or does it have some type of structure? What could possibly form a simple "off/on" switch for RFI based on RPM? Position of the governor?...that's a completely mechanical solution surely. And if the noise is frequency independent of the engine RPM then what is the frequency source for the noise?
Can you hear it on a handheld radio? If so you might have some luck sniffing for a source, but that's logistically formidable beyond sweeping the in cabin avionics.
Sorry, scratching around, just trying to give you new ideas.