Electronic – the definition of interference vs. noise in radio communication

I think you are picking up AM radio interference because of the relatively high resistances you are using. High resistances make it easier for a low energy signal like a radio wave to imnpress a voltage on a circuit. I would suggest 2 remedies. One is to reduce all of your resistors by a factor of 10. Why do you need to put such a large resistor (R4) in series with your output? Another remedy is to put a small bypass capacitor across R2 to filter out the AM signal. If you reduce R2 to 10k, then a capacitor of about 200 pf should be sufficient. If you reduce R2 to 10k, then use a capacitor of about 2000 pf.

You can shed a little bit of light on this by playing with the guitar (i.e. pickup) orientation. If some orientations are much noisier than others, then almost certainly it's the inductive coupling.

As to whether the interference is in the RF region and your amp is rectifying it, my guess would be no, but if you really want to be sure, try adding a small cap in parallel to the input of your amp, something like 100 pF (which will slightly affect the tone). If that gets rid of most of the noise, then it was indeed RF.