Denny, I used to be in the retail side of the tire game. I have mounted many a tire in my day and have used several types of balancers. Point is, I'm familiar with your problem. I admit I didn't fully read your initial post. Back in the day it was not uncommon to find a tire that was just too wackey to balance. Didn't matter how much weight or where you put it the tire/rim just would not balance. We would pull the tire and mark it with a big white chalk X and send it back to the manufacturer
(B F Goodrich) for warranty. If you are hanging more than 4-5oz weight on the wheel you may have one of those wacky tires. Hope you can get it corrected.