pet hate of mine this...easily solved 9 times out of 10 by rotating the tire around the rim 180 degrees and starting again
Mine too, drives me mad. I fully understand tyre places don't pay much and have low margins and I have time to spend getting it right. I've spent up to an hour getting a Land Rover rim balanced nicely.
I've seen wheels where they have weights 180 degrees apart, you can get odd things happen like when you do the test spin but when that happens I take them off and start again.
I big open wheels I always run split weight program and hide the weights behind spokes.