At the higher 6s voltage, the switching BEC could be "transmitting" more noise from the switching action. Given the close proximity of the BEC to the radio components/wiring, this could be causing errant noise getting into them.
Something as simple as wrapping the BEC in tinfoil may solve everything (make sure it doesn't short anything out!)
Also, you can try adding a capacitor to an empty receiver slot. 1000uF, 16v or more should be sufficient. This will help clean up any noise on the DC voltage. Also, wrapping the throttle and steering wires a turn or two around a
ferrite donut may help. This may help reduce interference from being induced on those wires.