The proper way to balance those wheels is with pin-plates, the adapters shown above from Hunter, Coats, Hofmann, Corghi, Bosch, Etc. Your wheel was without a doubt damaged by the first shop when they mounted the wheels using the plastic cup adapter with their balancer.
Also, just as an FYI to 09Nitetrain you shouldn't be outside coning a wheel like that as it may cause the balancer to chase weights, the outside of the rim is never made to used with a cone as the cone may not sit properly. Never mind the fact that the wheel could be lug centric vs. hub centric. I have balanced wheels like that myself until I started selling tire equipment almost 10 years ago & went to numerous training courses. I know you do what you have to do in a shop to get the job done but over 80% of the so called balancing problems we have with equipment & wheels is caused by improper mounting FWIW. Whenever I am on a sales or service call now & start talking with techs about balance problems I can usually trace the root cause back to improper mounting or cones that are beat up & dinged.
Good luck & hopefully you get your wheels taken care of!