Sorry if I'm not answering the exact question or repeating what was already said. Just going to give a quick reply based on some stuff I skimmed.
Some good strategies for showing frightened parrot to visitors:
A) No visiting/interacting with the bird immediately upon entering
B) Give parrot opportunity to sit at safe/undisturbed distance and watch while you entertain guests
C) Slowly place parrot closer or bring crowd closer
D) Interact with parrot yourself with visitors watching at distance (this way they can see how to handle and parrot gets used to being handled in their presence)
E) Target parrot onto people's hands one at a time (but no petting)
Don't feel that you must let visitors interact with your bird (though over time
socialization is good). If people want to hold your bird but you know it will be bad, don't feel obligated to do it. Bad interaction with guests will make the parrot much more weary of them in future.
You need to mediate any parrot-human interaction at all times. You are the bridge. You must make the parrot feel safe and make sure the humans don't do anything wrong. You should practice targeting your parrot on your own so that when you have visitors you can use the same familiar techniques to target onto their hands. With the target stick there, the parrot knows what you want from it and is more likely to cooperate in similar ways that target training was good to get the bird to step up for you earlier on.
If the parrot is mature and territorially aggressive, it is best to
perform these socialization interactions away from the parrot's area (better yet away from home). But if the parrot is young or not territorial, then at home is probably best.