Help needed - low resolution readings from ADC's

I would try to help the best I can:

- is such a small resolution common?

Well, if you connect your guitar (or bass) and play you will see that the signal does not vary much, this is normal, I think that its due to the fast variation that is not reflected in the serial port speed (which is relatively slow)
If you have a spare potentiometer, try to connect a potentiometer between 3V3 and ground and with the middle pin connected to the Arduino DUE ADC you should be able to see the complete sets of values when you swipe it (between 0 to 4096). You have to do it directly to the arduino pin, otherwise the pedalSHIELD input stage DC blocking caps will stop the signal to reach the ADC.
If you have any problem understanding this let me know.

- would swapping the 0.5 uf film capacitors back to 0.1 increase the resolution?

I dont think so, using 100nF with have a low pass filter of 15Hz (100K res + 100n cap), using a 500nf (or 470nF) the cut off frequency would be around 3Hz, allowing more low freqs harmonics.
The resolution would be the same.

- or is the small resolution caused by something different?

The ADCs are 12 bits, if you print the value through the serial port you should be able to see the whole set of values, but again if you just plug your instrument would look like you dont have much variation.

By the way, did you adjust the VR1 trimmer (the white one)? It adds gain to the guitar so maybe you have it set too low...