Well, I'm going to start just by telling you that disc brakes are very simple mechanical devices. I don't have the words for any shop that can't take care of squealing brakes.Not sure what to do
That said, if they didn't put on a dial indicator they might have missed a warped rotor because you just can't "see" that un-aided.
Although your problem could be one or more of only a few items, this is what I would do. Because parts are so cheap, and you will probably need them anyway.
Put on a new set of rotors and brake pads. You MUST do a few things at the same time.
1) Install new brake hardware. This is just what "they" call the brake pad guides.
2) Clean and lube the caliper pins.
3) Make sure the calipers, wheel hub, wheel face is steel brushed free of rust and dirt, then cleaned with brake cleaner.
4) Bleed brake system afterward.
Doing this will cover most anything that could be wrong. If you are going to do the work yourself, we can help. The one thing that many people fail the realize is that 95% of what makes disc brakes work well is keeping everything parallel.