An update: a very helpful private post lead me to unscrew the top turret dial. The small centre screw in this dial had clearly been taken off before. My suspicion is that the person who previously took off this dial then either put it back 180-degrees out of alignment and/or they may also have advanced the large brass screw underneath it, before replacing the dial. There is a stop that ensures the dial can only be rotated one full turn and, if they managed to get the ridge underneath the dial on the wrong side of this stop, that would explain why the scope could not be properly zeroed. With the dial removed, I was able to adjust the large brass screw below the dial a small amount so the replaced dial and its ridge now sits on the correct side of the stop. This means the reticle can now be adjusted to give me the correct zero. At the range this can be fine tuned if necessary.
I had exactly the same problem with another Drilling, so if you have a similar problem, this may be the cure if you proceed carefully.
