It sounds incredibly frustrating.
I've read the book just yesterday for the second time, and still struggling to use the techniques with my 11 year old, so I "get" what you are dealing with.
What I noticed was the way you praised dd for keeping control. Is that such a good idea? Perhaps she is beginning to think of herself as this creature which needs to be under pressure all the time. I would praise her for sounding out those words and for choosing a good book. She possibly doesn't want to even hear your voice, if she is like my son, who hates interruptions !!!
The challenge seems to be creating an external pressure too. Is it worth bending the rules for her and making the 20 book challenge 20 books she reads to herself without you listening to her read?
Asking her what she wanted to do is too overwhelming - so now you have a child who is anxious because she doesn't know what the solution to her problem is. She doesn't know how to solve the problem of the unread book and the tick on the bookmark. This is yet another pressure being put upon her, rather than an" invitation"
I would be discussing the book and the book challenge when she isn't about to read it, ie: in a neutral setting. I would make the discussion about how you get the tick, and what she thinks would be a good way to get a tick,( after all that is what she wants at this stage) Maybe she will say she doesn't want to read much of the book aloud because it is too hard, and you can say that is fair enough, and then you could ask her whether she would like to read less, and count the words or sentences and stop there. Maybe put it down in writing even and pin it up next to her bed, for her to see what the (minimal) plan is. That would be reassuring.
Then when you start to read, you already know what the plan is.
It also sounds like she is waiting for you to correct her (even if you are not) because she is anxious about her reading because of the fear of failing to get the tick, and that is why she explodes. She is waiting for things to go wrong, to be told off for not keeping control, and there is an inevitability about the whole situation that makes her more and more anxious and uneasy.
I am very interested in CBT (collaborative problem solving) and the way it removes the need for rewards or punishments. In our house ds2 has briefly responded to rewards and punishments (sticker charts, merits at school that sort of thing) but over the years it is mutually agreed systems and relationships with people that work the best. He gets dressed and comes downstairs when asked not because he gets a reward for it or a punishment for not doing it, but just because it is what we do . So in a way a lot of the time we use it anyway before we even heard of Plan B. It is just with the tricky stuff we aren't used to articulating Plan B to our children. We think the trickier the problem the more we need to lay down the law, whereas it is the other way round.
Good luck, I am feeling my way with this one on Ds2 and homework explosions and learning a lot in the process about his acute sensitivity to being interrupted or corrected or feeling inadequate. He gets there in the end, and he is always surprised how much easier it was than he thought and that feeds through to the next session. Still a long way to go though. I feel I need to reduce the demands on him, rather than try and get him used to demands.