Wow, you have been doing amazingly! Well done you! Yes, I agree with what you are doing! We do want to give control and show our children that we are user-friendly, attractive individuals who are easy to be with.
It sounds like with the books, your son is engaging you in a repetitious game. This would be a time to include some kind of challenge for him and see if he is open to it. I might ask him to look at me, as I say and point to each picture of the book, or to say the word "Read" when he takes my hand and shows me what he wants. You can also build from the book by acting out the pictures, singing about them or reading the word in different, fun character voices. If your son is rigid and controlling around it and insists that you read it in the same way each time and doesn't respond to the requests you are making, then he is not as connected and therefore not available to be challenged at this time, in that case, I would go with him and read it in the way he wants until he is more connected and open.
With the trampoline, are you able to get on the trampoline with him and bounce him higher? if so, then I would do this for a while and then work on language or eye contact as suggested before. If he doesn't need you at all and is happier bouncing by himself then join him by pretending to bounce on your own trampoline, My guess is that he is craving some sensory stimulation and it's helping him to regulate his sensory processing system. If you are not designating specific one to one Son-Rise time with him at this time then it's fine to leave him jumping by himself.