Hi,
As you do your testing and thinking about the signals getting into the audio section, you should know the audio amplifier is not picking up and amplifying the signal. The RF signal is getting into the circuit and being detected by a / some transistor or diodes. So traditional amplifier solutions will not work, the RF must be stopped before getting to the amplifier. This might have been obvious but I thought it worth saying.
Typical RF tools are:
- 100 or 1000 pf caps to a ground plane (on any wire going into the audio section)
- Series inductor (toroids) or ferrite on the amplifier wires.
- Physical shield (can, groundplane etc)
Not knowing your layout, it might be an interesting to short the audio input to ground inside the module and see if you still get you interference.