Rote learning takes time and repetition to work. We don't use a book here so ours is all mouth to ear for instruction, but I have used our monitor for learning parts for the long-form lectures. I'll try to pass along my thoughts...
When trying to learn your work, SAY IT OUT LOUD. Hearing yourself actually say the words will not only help to commit it to memory, but will also help by establishing muscle memory. It sounds silly, but I basically commit my morning commute to work (every single morning) to reciting ritual work. I really cannot stress enough how much better information is committed this way rather than just reading. For myself, as an EA I tried to learn both the questions and the answers, which helped lead me into my next answers. I used different "voices" for questions and answers. Helped to keep it all from running together.
After that, I suggest never moving on to another part until you not only have it down perfectly, but also comfortably. That is, no long pauses while you try to recall the words or stutters. When you can say it naturally, smoothly, at a normal cadence, like you're talking, then move on to the next part.
Speaking of cadence, establish one! Don't try to spit all the words out as fast as you can. The cadence, that is, timing, that you make yourself speak at will do wonders in helping your mind to establish a rhythm to your words and help it to come out smoothly and easily. Use inflection and emotion in your words. Proper emphasis on parts that are important or cause you problems will help distinguish them in your mind.
Use mnemonics! Even for simple lists or items you have trouble remembering, establish a memory device that will help you recall it later even if the actual mnemonic is silly or doesn't make sense (ex. I made up and use the phrase "weasel manufacturer" as a mnemonic for a particular part, it would make no sense to anybody else, but it helped me once upon a time and is unique to me).
Also, be visual. Try to tie what you are saying to what you are seeing, even if it is not the entire picture, maybe a detail that will trigger the right words, heck it may not even be related to what you are saying. A visual mnemonic of sorts.
As you learn a new part, start from the beginning, every time. That way you say the beginning parts SO MUCH that your brain can spit them out without even committing thought to them, it just knows them.
Good luck!