I've done something similar. I think I would say maybe differing in that my dog does not have extreme drive for his ball but he has drive.
He does not care to be touched by strangers but that's not extreme either. He will gladly deliver a ball to a stranger and play with them. If they try to pet his head during this he will duck back slightly with a very meaningful look at the ball, then to their face. It is very clear to me that he is mildly annoyed that they want to delay the game of ball with this stupid head petting nonsense that he sees no point to.
Anyway. I taught the sit for exam first, and we are still working on stand for exam but he'll have it soon. I have done progressive stays with distraction with people approaching, close enough and focused on him as if to touch but not touching. When he had that we moved on to touching. First time I do it with his ball on rope for focus. I know they are scenery to him because what he really cares about is the ball. Then I immediately do a rep with no ball in front him and last rep the ball is across the room and I release him to it when I am done and happy with what he did.
Basically I have taught him that in the context of working obedience, being touched by strangers is an obedience exercise and after so many repetitions he understands that it's just this predictable touch and he is totally fine with it. They never grab his face or get in his face like stupid people petters try to do sometimes, they never do painful or invasive stuff like the vet sometimes, and it is just another distraction that he ignores while performing obedience. He glances at the judge when they approach but in his mind they are still scenery
I did do one training session with some strangers and after he had done a very nice exam, I released him to the ball and then allowed him to go to give his ball to the strangers who had done the exam. He is motivated to try and get strangers to play with him because he learned during some construction on our property that strangers don't follow mommy's stupid safety rules and wing balls at 100mph down hill and it's dangerous and fun you see. So being released to try and get these people to be his rule breaking ball slave was actually a big reward for him and it helps bridge the gap with strangers for him.
At this point he has been very consistent for a fairly long amount of time and I've recently competed him in a very new environment with a brand new male judge who did the exam and he was flawless. He gets more and more confident as we go but I continue to tell random people not to pet him because he just doesn't get anything from it and sometimes they make him uncomfortable. He does make friends quickly and easily with people he sees regularly in his life and becomes affectionate with them and then enjoys being touched by them so I feel like everything is fine and good.
I have never used the ball to deal with the vet. I think it might pollute the ball for him because he doesn't have THAT much drive. I have adopted a no nonsense you have no choice in this matter with him same as certain handling at home. He won't take food from strangers and has zero desire to be friendly, but he will go in with me and tolerate everything. He does not resist, evade or be nasty. He would rather get the heck out of there but he understands this is another thing, like ear cleaning, that I am going to make him do and I expect him to conduct himself a certain way and he has no choice. That's the important thing. if they try to make friends with him or get him to choose to cooperate, it's much worse. He isn't going to like it but he will behave, and anything wishy washy just makes it so much worse. Come in, get your hands on him, and get it over with and there will be no fuss. But don't try to get him to be your buddy. He isn't and won't be. It actually freaks him out when people in situations like this try to make nice with him. It's like he thinks it is a dirty trick because he knows they will stick the thermometer up his butt. He does not want them to try to be his friend LOL
His behavior at the vet has gotten much better and is consistent at this point so I think what I'm doing is the right thing for him