master of none is correct about nonsense words - they aren't a skill that's taught, they are used as a way of testing a specific type of reading skill that is useful in diagnosing reading disabilities.
Susan, I don't know what the answer is for you re is the learning center investment worthwhile, but both of my daughters struggled with reading. I'll tell you a little bit about both, since each touches on your situation but in two different ways. To summarize before I bore you with the details, both daughters had different issues that impacted their ability to learn to read, but in both cases it was really important to understand not just what areas they were struggling in but *why* they were struggling - what was causing the lag in those areas. Although the challenges they both had/have showed up first in learning to read, reading wasn't the challenge, it was a different skill that was called upon in the process of learning to read. So that's my potential gotcha for entering into a program to remediate reading skills - are you sure you're addressing the real challenge.
My dd10 was identified in first grade of being at risk for a reading disability by the school and referred to a multi sensory learn-to-read program. We chose to send her to a private summer school program and she was given most of the same tests you've listed above as part of her intake into the program. I don't remember anything about her specific scores, except that they indicated she needed help and one note from the tester that she copied from the board in a very odd manner as well as a note that she was easily distracted by noise - much more so than the typical child. Her teacher felt she made progress that summer (we saw a tiny bit of progress but it was very very slow), and her teacher also noted that our dd was an auditory learner much more than a visual learner. That was probably the most helpful piece of information that came out of all the work dd did that summer, but it didn't occur to us at the time to wonder *why* she was an auditory learner. The next year in 2nd grade back at her regular school she was struggling even more and we eventually took her in for a full neuropsychological evaluation, where we learned that she was having some rather severe difficulty with her vision (her eyesight was 20/20, but she had double vision, one eye shutting down to deal with it, troubles with tracking, and extreme lack of peripheral vision). She went through a year of vision therapy to address those issues and by the third month her reading ability just took off like wildfire.
Our dd8 also struggled with reading, but she's HG+ (older dd is MG), and was doing so well in school overall that it wasn't until 2nd grade that her teacher saw what we were worried about at home - her reading ability was lagging far behind what we all thought she should be able to do based on her verbal communication skills. We didn't have any concerns outside of reading, so instead of taking her for a neuropsychological assessment we consulted with a reading specialist who administered cognitive/achievement testing as well as dyslexia screening tests. What we learned was that the challenge for dd8 wasn't reading but was a large discrepancy between her overall cognitive abilities and one intellectual ability which severely impacts her associative memory - so even though it seems like she learns by visual means, she doesn't remember things she learns visually in any reliable way. It was recommended that she use audiobooks for school as well as remediating spelling using auditory programs rather than relying on visual learning.
Best wishes,
polarbear