What I actually said was just a quote from the Shure Corporation white paper on static charge. They observed that if you neutralize only one side of an LP the charge on the other side will migrate to the treated side. I would have to review that paper to recall under exactly what conditions. Your finding that both sides are discharged by treating only one side is surprising, but I didn't measure the untreated side when I did my experiments, so I am in no position to disagree, apart from quoting from the Shure paper.
I will also say that in my own experiment, using a ES charge meter to monitor results, I only aimed the gun at the label from a distance of about one foot (not 3 different spots), with the trigger fully depressed. (Now my memory is playing tricks; I may have brought the gun to the LP while also depressing the trigger slowly, or not.) Then I gradually released the trigger while also slowly moving the gun away from the LP until at about 3-4 feet I fully released the trigger. This reduced the measured charge on the treated surface from -11kV to around -0.2kV. It is not clear to me how you are using the gun; at what points in relation to the LP surface do you squeeze then release the trigger?