Can't tell about Emeralds - never played them - but how your tone cleans up with the volume pot depends not only on the pup (and electronics), but also on the amp, gain pedals (if any), and how you setup your gain(s). My own experience is that I get way better results on a crunchy vintage amp pushed by a low-gain OD setup for dirt boost than on a more modern hi-gain amp set up for approximately the same amount of distortion (without any pedal) - and this with any of my 'buckers (RR, ABomb/Mule, Crawlers).
Not that I don't have some cleanup on the hi-gain part of my amp nor that all pups clean up the same (RR and ABomb bridge, which are rather bright and not much "compressed", tend to clean more than the Crawler), but the main difference wrt/ cleaning up with the volume pot obviously comes from the gain structure - FWIW, on some hi-gain amps I tried, I just couldn't get anything but mush when rolling down the guitar volume.
So the question is: did you try with 1/same amp, same settings, different pups and b/same pups, different amp ? And if yes, do you still have the same problem ?