My DD20 who's in college has a language processing LD. She was officially diagnosed in 2nd grade. My daughter didn't have the phonological processing problems your daughter is having she most had comprehension problems. She could read individual words but couldn't really tell you what whole sentences meant and often she would skip over words that she could read just wouldn't notice were there. She did get help in school with IEP but I also ended up having her work outside school with an educational therapist who specializes in kids with reading and language delay's. My daughter worked with this therapist outside of school for 15 years and it really made a huge difference. The trick I found is to find a specialist that trained to work with students with LD's.
One thing I found was that school didn't really know how to remediate for DD's specific problems. I found at some point that in school they were spending a huge amount of her time with the resource specialist reading the same passages over & over again until she could read them fast. What they were using with her was geared towards fluency more than comprehension. Took the outside specialist to point out that this wasn't what DD needed.
Good luck.. Schools can be really blind to 2E problems until the kid finally fails to keep up in older grades. It can be really frustrating. I do think you should still push the school and if you have resources I would look for an educational therapist or a program that works with dyslexic students.