Shielded interconnects would be a first step.
I lived through RFI hell for months. The first problem was a cheap wall wart for the HRT iDevice. Then I removed the iPod from the system. The final solution was using Ferrite beads on all ICs and speaker wires. It is an interesting dilemma. All solutions vary. It will take longer to solve if the source of RF, i.e. radio towers or an apartment full of routers, is highly visible.
Just a thought::
IF the volume of the radio station doesn't change with changes in volume control level, that would tell me it is coupling in AFTER the preamp gain stage, which would presumably change the level of the RFI, as well. The fact that it is coupled for ALL inputs helps that conclusion.
Perhaps rearranging speaker wires would help. NO coils, for example.
Do you know where the radio station's transmitter is located? How far? How much power?
If what turns out to be the antenna is at right angles to the transmitter, that will be the orientation of maximum sensitivity to the offending signal.