Ive been fighting the balance on my 47 or years now. I still cant find a tire shop in this county that can fit a 47" tire on their machine and properly balance my tires. After years of discussion about what to do with 40+ tires a ship builder gave me this method, it turned out to be amazingly precise. and pretty quick. Now all I have to do is dismount the tires and glue the balance pads on the inside. I made the balance jig so that the pivot point of the tool was in the exact location of the center of gravity of the tire thus the wheel offset did not effect the balancing. the best tire took 1 oz and the worst took 20 oz. that would have been 60 oz on the rim due to the difference in rim radius vs tire tread radius. So by putting the weight at the exact opposite of the heavy side, far much less wight is required, and you don't have wheel weights coming off in the rocks.
Here is the same tire hanging in balance with the balance pads thumbtacked into position. I used a paint marker to outline the position of each one so it can be glude inside the rim. what amazed me through this whole process is that just moving a pad a 1/4" makes a huge difference in balance.
This is one of those deals where having a lathe and a welder means never having to say you are sorry.
I did some math to determined that with my 12" wheels I had to be 2 1/2" from the back side to get to the center of gravity. So I welded a 2" long piece of 1"dia. Al to some scrap 3/4" plate. then I chucked it in the lathe on the 1" piece and took light cuts till I had the correct id, .005" under the wheel ID at 1/2" wide, leaving a 1/4" shoulder. then I drilled it 1/8" through the center for an 1/8" cable to go through.( note:ignore the flat on the shoulder, as the piece of scrap I used was not big enough to get full round so I split the difference and there is a matching flat on the back side of the picture you cant see, but by making it symmetrical It does not effect the balance.) I used a piece of 3/4" plate aluminum, roughly 5" x 4" and then sawed it round as I could prior to the lathe work. I'm sure you could make one out of steel as well. as long as everything is turned symmetrically it would not effect the balance.