Welcome and thank you for taking the time to share such a lengthy story so we all understand the situation a bit more. . I would keep this bird as comfortable as his lead shows you. If it were me, he has many new things to get used to, and keeping his surroundings in his cage that he likes will only help him feel comfortable quicker. I would put his favorite rock back, it comforts him, and as my rescue cag did, over time, she began to leave her comfort perch and venture onto other things and never uses that perch any more even tho it's still in her cage.
As the others have said, it is too early to try much with him, just let him get used to his new environment, before you try to do much with him, let him lead you and learn that it is okay to trust you. He is afraid and doesn't know that you, a stranger means no harm to him. That takes time for him to understand. Remember, he doesn't know where he is, why he is there, who you and your family is, who these other birds are, what the sounds of
your house is, and doesn't know this is his forever home. Just be kind, don't push him and he will start to venture out of his protective shell on his own once he realizes this new home is safe and loving. Please keep us posted, I look forward to hearing more, and seeing pictures...