It sounds like your dd has a fine motor coordination challenge. If you look at the WISC scores under processing, she has a lower score on coding - this is a subtest which has the student make marks in specific directions with pencil and it's timed. The *very* low score on fine motor on the Beery is another indication of a fine motor challenge.
Like Zen, I have a child who has visual processing challenges - but fwiw, she did *not* score well on the Symbol Search subtest - that subtest has you look for specific symbols in a randomly ordered highly scattered page of many many drawings. Since your dd performed really well on that subtest, I'm less likely to think it's a visual challenge.
My ds13 had a diagnosis of Disorder of Written Expression when he was in 2nd grade, as well as fine motor dysgraphia (and a misdiagnosis of ADHD, fwiw). He also has a dip in coding and a strong score in symbol search on his WISC testing, and a low score on fine motor on the Beery. I *think* he had a not-so-stellar score on the Beery visual subtest too, but can't remember for sure - when I have time later today I'll look it up. FWIW, he has been evaluated by a developmental optometrist and visual issues were completely ruled out. My ds did have some additional testing as part of his neuropsych - executive functioning, attention (can't remember the name of the test), and fine motor tests (called "finger tapping", part of the NEPSY) to tease out the results of the WISC and Beery.
The thing I'd recommend you do write away is to chart your dd's WJ-III Achievement subtest scores against the type of *response* required on each test. Some have oral response, some have written responses but aren't timed, and some require written responses and are also timed. For my dysgraphic ds, his WJ-III Achievement scores *appear* to be all over the place (and not so impressive) until you graph them that way - then a very clear pattern shows up - the oral response subtests track the percentile that his IQ is in, the written but not timed response subtests fall about 30 percentile points lower than that, and the written+timed subtests all track each other but at a very low score. Soooo... what you're really seeing with ds is the impact of his fine motor challenge, not his ability in the specific skills that are being tested. It would be interesting to see if a similar pattern comes up in your dd's achievement subtest scores.
Re the diagnosis of "Disorder of Written Expression" - my ds lost that diagnosis when he was reevaluated at 10 years old - even though he also has an expressive language disorder that impacts his ability in written expression. When I asked his neuropsych why she dropped that diagnosis, she said it was specifically because his scores rose in one of the writing subtests on the WJ-III. I can't remember which one, but if I have a chance I'll look back at his two sets of testing and let you know - I'm guessing that particular subtest score is going to be low for your dd.
Re the Grey Oral Reading scores - that's one I don't know what to think about. I've had some questions over the years re is my ds stealth dyslexic, even though he reads at a really really advanced level and seems to comprehend well. He's never had the Grey test, but he fits some of the other profile symptoms the Eides include for stealth dyslexia. I have a younger dd, however, who does not have a challenge with fine motor skills or written expression but has struggled to learn to read and has been identified as having a challenge with associating sounds with symbols. She's had almost every reading test under the sun, including Grey, but hasn't seen a neuropsych yet (she will this fall). Her scores on the Grey are a similar difference as your dd's percentiles between IQ and Grey. She is not dyslexic, and she scores well in some of her reading assessments, average in other areas, and really really low in that one bug-a-boo of sight-symbol association. She much prefers to listen to audiobooks over reading, and she does not like to read aloud. I only mention dd because, fwiw, getting to the root of what's impacting her in reading has been *very* challenging, and it's also been very challenging because we see what we think are impacts of it across the board in her schoolwork and testing now, yet nothing stands out as clearly obviously correlating with an obvious diagnosis like dyslexia. Determining what is up with our kids can be *tough*!
The other thing you can do (if you haven't already) is to simply write down every detail you can remember of your dd's developmental history (before school) as well as academic challenges. For my ds, some of the things we thought were just cute quirky things when he was a toddler etc were actually signs of developmental delays that related to the reason he also has a fine motor challenge - none of that was clear to us but his neuropsych put it all together for us and *then* it was "obvious"

Last note, difficulty with spelling and punctuation are potentially symptoms of dysgraphia, which I would strongly suspect based on the other test results and what you've written.
Hope some of that helps!
Best wishes,
polarbear