Welcome!
There are a few families with relatable experiences here. I expect you'll hear from them shortly. My position generally as that, when skills are this diverse, one should decouple the skills, and work on strength and vulnerability areas separately from each other (even when they appear closely related, such as in written expression). In this case, the value of continuing to work on handwriting depends on many factors, including the severity of the visual motor impairment, and the true underlying deficit.
A few more questions come to mind: deficits in both phonological processing and fine motor skill suggest that this is not just about hand skills. Does she also have a history of articulation/speech issues? How are her other fine and gross motor skills (ball skills, early milestones, swimming/bicycling, etc.)? Is there a history of other discrepant or asynchronous automatic skills, such as delays in learning math facts/math minutes (even orally), or achieving reading fluency?
I'm asking these questions because they can help fill out the picture of whether intensive, repeated practice generally pays off for her, or whether there are underlying deficits in automaticity that suggest that her time might be better spent learning to become a fluent typist (especially since, if automaticity is an issue, that make take longer than expected, too). (And, FWIW, my mother moved my sib to typing at eight, because handwriting was such a hindrance to otherwise extremely rapid academic progress. So I don't think nine is too young.)
My personal practice wrt written expression, as I mentioned above, is to teach and assess the skills separately. So there might be a little time devoted to handwriting per se, but then the remaining written expression tasks would be scribed or speech-to-text. The criterion I use is: what is the key learning objective of this task? Is it handwriting (then handwrite), or is it language expression (whether it is grammar, ideas, organization, etc)? If mandating a basic skill turns your exercise into a measure of something other than the alleged key learning objective, than scaffold the basic skills until the learning focus is truly the focus. You can always work on the lagging skills in isolation.
BTW, I would be cautious about this phrase, "a lack of persistence for tasks that require effort." If her verbal cognition is above the 99.9th %ile, but her handwriting is two to four years below her age level, then forcing her to write by hand is not just making her do a task that requires effort, but an absurd difference of something like six or seven grade levels between her oral expressive language and her handwriting ability. Learners at the K/1 level are still thinking about letter formation and spacing, let alone spelling and grammar. Put yourself in her place: try writing a five paragraph essay from scratch (no pre-planning), using your nondominant hand (and maybe using only the mirror reflection of your writing, if you happen to be a person who has practiced writing with your nondominant hand). Then decide if refusing to write what she can think is truly a lack of persistence.
