In a lot of ways, the things you're describing - sensitivity and the desire for repetition and inane series books - are very much age and developmentally appropriate.
We dealt with it in a few ways: I announced when DD was 5 that I needed to enjoy the books I was reading as well, and so book selection had to be done jointly.
*Certain books were ok for her to read over and over (and over and over) as "in your head only" books. The @#$%$ fairy books ended up being what gave DD an incredible reading stamina and launched her into a greater love of books. But in her head only.
*I matched DD up with a children's librarian and had the two of them find books. I found that taking the mom-kid dynamic out of book selection stretched DD quite a bit more.
*I "hot housed" a few literary terms & concepts, introducing foreshadowing, climax, and other parts of story telling to have DD anticipate the path of the story. I first used this in Charlie and the Chocolate Factory, where I otherwise feared her reaction to the story.
*I read the first few chapters of a book to DD when she's otherwise trapped: soaking in the bathtub, waiting in the doctor's office, etc. I don't spent a huge amount of time talking about or selling the book. I just start reading. She'd either be hooked after the first few chapters, or she wouldn't be hooked. There are tons of books in the world, and there isn't much point in continuing on one that doesn't grab you after you've given it a try.
*We've had good luck with the American Girl series: they are decently accurate history, generally featuring a 10-ish year old girl with some sort of talent, with very tame plots. Avoid the Addie series, which was not tame. We moved from there to Dear America and Princess Diaries (similar quality. really.), though we used the librarian to sort through the appropriate Dear America books for sensitivities.
