Have you tried a magnetic pickup coil instead of the electret microphone? If the phone is hearing-aid compatible, there should be sufficient magnetic energy present. With this approach, there would be no direct acoustical sound picked up.
Even if you could completely shield the pickup or electret microphone, you must also shield the cellphone's microphone. A percentage of transmitted audio is fed back to the earpiece to give the user confidence that they are talking loud enough, and that the phone is working. That percentage is called "side tone". The side tone would contain any background noise, and would be coupled to your pickup or electret microphone along with the received audio.
Put it into a small metal enclosure, with some very small holes in it to let the audio in. The metal enclosure needs to be connected to the ground braid on the audio cable.
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