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Agreed on most of this but I can say with almost certainty...the lug studs are a very "soft" steel...actually it is very ductile.
Most likely you will need to remove the good lug nuts first. Then attempt to remove the the bad ones once at a time. I usually suggest using impact but in your case try to get a lever against the back of the stud an loosen.
My guess, one is toast...maybe two ut even the most moronic of impact wrench monkeys would not have time to mess up three.
Getting the lug studs out of the rear is actually very easy. Lug nut threaded on flush to the stud. 5 # hammer (3 # if you feel lucky) and on very firm, well placed whack. Rotate the hub until you find the one place it can be extracted from the rear of the hub (disc has to be removed as I remember).
Will in increase the chance of the hub bearing being damaged...sure. Is it worth the the risk...yep.
In the future there are a number of options to mitigate or avoid this. You will NEVER get a tire shop to change their ways so:
Always bring in bare wheel when possible
Every time you remove the wheel, wire brush...if any resistance going on or coming off, replace the lug nut and use a thread repair split die on the stud
When you do have to let the tire or alignement hop handle your car ask to see their 65 ftlb torque sticks BEFORE you reliquish the car. When they cannot produce them, then indicate that due to the lack of the proper stick for the impact wrench they MUST use hand tools and their disclaimer on the wall (point at it) is not valid if they do.
No matter what, before leaving the parking lot, loosen then torque the all the lug nuts in full view of the garage.
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