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.
I know just where you're coming from, I worked in the retail side of tires, too, until about 6 months ago (shop closed due to corporate idiocy). These days, the make you drill two 1/2" holes in the sidewalls of a warrantee tire, to prevent it from getting mixed in with good used casings that get retreaded in Mexico.
Denny, I see what you mean with your situation. We were pretty good about taking care of balance issues, even to the point of setting up appointments for customers with a problem that couldn't be solved by the tire techs to have the alignment/brake/diagnostic tech (me) take the time to check the problem and solve it as necessary. But some shops simply don't want to put the time into taking care of issues like that.