> Your first problem is assuming that the "power is dirty". Electricity isn't like a water supply that can get contaminated upstream.

A friend with an EE background when asked to listen offered the same conclusion, and went on to say:

The thing is, "dirty power" is not a bad description.
The power is supposed to be ~12VDC.
It sounds like the power is actually 12VDC plus an AC component whose
frequency varies with engine speed. This could be tested with a meter
but that shouldn't be necessary.
If that is the case, then regardless of whether the AC component comes
from an electrical problem or RFI, a suitable capacitor (filter) should
eliminate it.

But it's easier to try the "power direct from battery" since I have all the stuff I need to do it in the car here at work with me, so...