I am going to go against the company's recommendations here! My son did AAR because of his APD and does like the readers. By now, since she has finished 2 & 3, she should have the tools to be able to read most books. My son is completing level 4 right now and it is finishing up phonics but honestly, we probably could have not done level 4 too. It is mainly sight words.
If it were me and I were you - I would stop using AAR and have her read through the early readers and go through the alternative titles. At that point, if she is still struggling with reading after this year, then I would invest in level 4. But even if you buy level 4, I would only buy the teachers manual and the student sheets. Skip the readers. If she hates them, don't do them. They are basically glorified later emerging reader books anyway IMHO. I share this because I am having both of my two youngest go through AAR. My son with the ADP does it all. But he loves these books. My 6 year old can read very well but she hates the readers. I have her listen to the lesson, then she reads the fluency sheet (level 4 is MUCH lower key and much less for the fluency sheets than level 2 & 3), and then she is done. AAR takes my two kids at the same time about 10 min total. Then my son will read the reader on the days he is to read. My youngest never reads the reader. She reads well and is reading most of Little Hearts to herself. I only have her sit with us during AAR because I don't listen to her read much out loud and I want to see if she can read. She always reads it right and well. Plus she can tell me everything that happened in the books she reads so I don't listen to her much.
As for my son who struggles though, I found that he "could" read the level 2 books even after finishing 1/2 of level 3 but if he made a mistake, he would keep making that same mistake over and over and over again. For him, he loves AAR so we are doing level 4 now. We are about 1/3 of the way through. Once we are done, I think he will be flying through the Level 2 books. He has already read a couple of them but we will finish the rest once he finishes level 4. As for my youngest, she reads whatever she wants this year and she loves to read. I haven't really pushed her one way or another because she is very particular about what she wants to read. I also know that for my oldest, in 3rd grade is when we spent quite a bit of time working on the reading. I would sit and listen to her a lot. We would break up her reading during the day and she was reading for about an hour a day. Sounds mean but no one complained. They knew what was expected and I was very patient with them. If they missed a word, then we would analyze it, go over the rule, break it down - my son goes to the tile board a lot. For my oldest dd, if she finds a book she loves, she will work a lot harder to figure it out than if it is a book she hates. Preparing ended up being her cure for loving books. She LOVED those books. I think because we did Preparing last year, she was so excited about what she could discover in a book and couldn't wait to tell me. Even this year, she loves the Zoology book. It takes her about forever some days but she loves it and she works hard and doesn't complain. The history book is also one she enjoys (not as much as science) but she always comes to me after reading and says something like, "Mom, you are not going to believe this........." It is good. I feel like she is empowered to take responsibility for herself with her school books, she likes this feeling and she has risen to the challenge.
So I guess if it were me, I wouldn't worry so much about perfectionism while she reads. I would have her read to you things she likes right now. I would drop the reading program. If the book is harder, I would have her read a page, you read a page, her read a page, you read a page for now. Find something she loves! She will then want to sit and read with you then. I did this for a year with oldest dd and we would spend about 45 minutes to an hour a day reading (broken up of course). While the emerging readers are great books, if your dd hates them, then I might even deviate if you need to just to get her excited. If you have finished level 3 of AAR, then your child should have the phonics they need to read most of the emerging readers. If your child doesn't like them for some reason (maybe because she older she may not like some of the books but ds recently just picked up Tornado and read it for 3rd time....yes, he loves that book

) then have her read something else. My kids all loved the Little House on the Prairie series. My oldest would sit in her bed 2 years ago and re-read those books (we read at night to the kids before bed time - this series has been one my kids adored). My oldest dd also loves biographies - she has read several of the young patriots series. My son loves the Nature Readers from Christian Liberty Press (he read the one last year that is in the Emerging Readers set and begged for more). My oldest likes mysteries, biographies, historical fiction, and folktales mainly. My son likes non-fiction books and biographies the most. My youngest - I haven't got her figured out yet. She seems like she likes fantasy and non fiction but she pretty much likes everything so far. I would just try to ignite a fire
It may not feel like it but it seriously sound to me like your dd is right on the verge of getting it and getting well. Don't give up! Don't feel hopeless! (That was me - I felt SO hopeless and felt like I was failing my child!!!) She will get it. Just breath and let her go at her pace. And we read over the summer too. Not sure if you do that but I really couldn't take that time off or my kids would forget how to read.