That could be caused by grounding loops. Try to connect each module's GND wire to a good decoupled "single ground point" ("star" topology). Maybe a decoupling of each module's power (small resistor in series and capacitor to gnd) could help as well.
How are you powering the board? I had extreme noise on a Bluetooth A2DP module connected to a Due, which turned out to be caused by powering the board by USB. When powered by a 9v battery into the DC jack the noise disappeared.
I've tried powering the board using both the USB and a 9V battery and using a star topology for ground, but the noise is still present. I haven't tried decoupling each module's power yet, but I'll try that next.
Hi bglsmith, any progress on this? I'm having the exact same problem an I've still had no luck getting rid of the ground noise. I didn't try decoupling though, did it work for you? Any help would be greatly appreciated, thanks