Echoing polarbear: processing speed is a symptom, not necessarily a specific condition. Many different factors affect processing speed.
In your DD's case, her processing speed is not motor-dependent (per low decision speed score on the WJ; processing speed test with minimal motor demands). That score also does not reflect reversal errors, as the images used are not symbolic. With what you describe of the teacher's report, and behaviors like picking up too many objects and reaching around the glass, I would suspect that the direction to look on a neuropsych would be executive functions, as many of these are related to planning and organization, and probably either encoding or retrieval as well (with low math fact fluency, and her early history of reading delays).
What math fact fluency, early reading, handwriting, spelling, and reading music all have in common is that they are arbitrary symbolic systems which one must master before one is able to engage in meaningful, relevant activities with them. (I suspect that she has not mastered handwriting, in spite of its lovely appearance, because her actual application of handwriting is so much poorer than when demonstrating the skill in untimed isolation.)
She has exceptional reading fluency now, most likely, because she finally acquired enough reading vocabulary (whether by sight, or by reaching automaticity with orthographic mapping/phonetic decoding) not to have to work out each word as she is reading it. I wouldn't be so sure that she is not a very well compensated dyslexic. You note that spelling is one of her primary weaknesses. That is very telling. If she is a compensated (stealth) dyslexic, she will probably need explicit instruction in spelling in order to close the gap between her reading and writing vocabulary.
To your original question: whether her processing speed will improve/normalize over the long-term on formal testing depends on why it is low to begin with. It also isn't nearly as important as whether she can learn accommodations such that she is able to reach a point in her life where it is not an obstacle to achieving her happiness or accomplishing her goals. The answer to the first is unclear. The answer to the second is yes, but it will be easier to attain if she has a clear understanding of her personal profile.
Last edited by aeh; 02/28/16 12:39 PM.