My DGT was wired incorrectly from the factory and acted similar to this. I found that the pickups were wired in parallel with the selector switch and output jack and wired incorrectly. So instead of the pickups hot going to terminal 3 and outputting on terminal 2, Mine had the pickup going to term 2, term 1 grounded, and term 3 grounded via the 10 Meg resistor and terminal 2 also going to the selector switch. On 10, the volume pot functioned because the pickup was going directly out via the selector switch. Roll the volume back and the pickup was heading to ground on one side and to ground through the 10 Meg on the other. It acted weird for sure! I rewired it and informed CS of the error and was surprised that their response was that I would void the warranty by repairing my instrument- I was hoping for a hat!
Maybe look and see if yours is wired funny. Pickups should go to term 3 out to switch on middle terminal with term 1 grounded.