These things strike me as being fairly trivial, or things one can trot out to continue to "shop" rather than actually get down to work.

If you're late to session, of course it's going to be on your time, not his time or the next client's time.

If he repeats things or otherwise engages in statements or actions that are not helpful to you, then a little communication about that goes a long way. Hey, dude, you don't need to repeat something more than twice. Is it possible for you to turn off the timer? Have a conversation about it. A reference book with a standard list of questions about depression might be expected during an early session, as another way to see that is he's being thorough in assessing your depression, rather than just knowing about what you spontaneously focus on. Gives a fuller, more accurate picture.

Maybe as the Buddhists say, when the student is ready the teacher will appear. I think it is your right to shop around as much as you want to, and it may not be useful to you to reflect on your reasons for shopping. Likewise, it may not be useful for you to consider how you might be able to change your communication style or cognitive beliefs about therapy and therapists to be able to work more effectively with any therapist. Maybe you don't need to use this process to figure out how there might be ways that you communicate, or don't, that impact your ability to connect with other people. But it just seems to me that there ought to be more than complaints about timers and reading from a book after going through 8 therapists.