OK, your mention of the fuel pump got me thinking...low wing right? So there's going to be an auxillary electrical fuel pump also...that's going to always run at a constant speed regardless of RPM...question is when is it on? I'd have thought it would be a manual switch only but I'm at the edge of my knowledge base here.
The fact the handheld doesn't hear the noise eliminates something, the noise is not "inband" in the VHF range. Such a typical noise source would be modern and microelectronic/digital in nature..anyhow that possibility is eliminated in my mind now. The handheld most likely doesn't hear the noise source because the internal design of the radio is completely different and so it's potentially sensitive to different frequencies of noise.
(Typical radio designs transform the signal several times to different
frequency ranges before it becomes an audio signal, and each stage generally has a filter that only passes on a certain frequency range to the next radio stage. These frequencies are typically referred to as IF - intermediate frequencies and are generally much lower than the RF signal you are listening to)
I take it the replacement radio's you tried were the exact same design/model?
I am still bothered by the directionality you report....the direction of the noise source relative to the radio/antenna position should not be changing regardless of the position of the station you are receiving.....so why do you only hear the noise when the station is in a certain orientation?...there is only a single antenna per radio, right?