"there are many statements made that the coils of this Humbucker are balanced."
are those people saying the pickups sound balanced or have a balanced voice/character/tone? or are they saying the specs off the meter show a balanced wind from one coil to another?
The statements are usually based on DCR.
Chasing DCR can be a fool's folly. Two coils made with the same wire off the same spool can have the same # of turns and have different DCR. Any one or combination of what was suggested (in the below quote) can apply, as well as any one of countless other oddities that really don't add up to a hill of beans.
At the end of the day, it could be simple. One coil was made on one machine by one winder, and the other made on a different machine by a different winder. Or one was made on Friday afternoon, and the other on Monday AM after a fresh calibration of the winder. Or maybe a setting shifted and the pitch or tension were tweaked. Or it was the same winder on the same machine made back-to-back with the same settings, but one coil was the end of a spool of wire and the other coil was from the beginning of another spool. Or the winder did one coil before lunch, came back to do the second without getting all the sopressata washed off their fingers and it got on the tensioner felt.
I would have expected more consistency and repeatability from a series production like DiMarzio. I'm not a professional winder, just wound a few pickups by myself because of curiosity. Using a very simple winding rig and guiding the wire by hand, I have managed to wind coils that are really close to each other (DCR, Inductance and Capacitance). Would be strange to me that in a professional process there is that much variation.
and yet the late 1950s PAFs from Kalamazoo are some of the most coveted humbuckers out there.
those were made to a timer, not a counter. a few seconds off could be dozens (or more) of turns on the coil. they were tossed in a pile and an assembler down the line would just grab whatever off the top and put it in to whatever slot in the guitar.... no "neck" or "bridge" designation. the materials used was whatever was available that day/week/month... could be alnico 2 on this batch and alnico 4 on that batch and alnico 5 on another. the facility didn't have climate control as we know it and environmental concerns were like the wild west back then... so you could expect to find a steaming hot big room in the summer with the windows open and no a/c with a bunch of ladies smoking their unfiltered Camel cigarettes while winding with the ash tray (if there even was one) within inches of machinery that was pumping out pickups that some people are paying thousands of dollars for today just to put in a guitar that hangs on a wall in some lawyer's home office and gets the dust wiped off more than it gets played.
I'm not here to defend defend DiMarzio by any means. but I might suggest than most current big-name pickup makers have consistency, repeatability, and a professional process that we might consider would blow away the conditions currently priceless Gibson humbuckers were made under. I think Larry is a jackass and he should replace his office staff with ladies that don't have to ride brooms to work. just as it's my opinion the Carter Duncan Corp (Seymour doesn't own it... and he's retired) is ran by a cabal of buffoons that I wouldn't trust to operate a deck of cards. and even so, they seem to do well enough to be above the scrutiny of a set that you happen to have that has a spec that you don't understand.
with all encouragement to your efforts..... wind yourself a few hundred pickups (literally) and discover what anomalies you encounter along the way. I'm guessing by that time that this random coil will make more sense by then.