The WIAT-III is an achievement test, so it measures learned skills, and yes, it does correlate with the WISC-V. However, it is not accurate to say these scores are not commensurate with ability. Other than math fluency, they are all within the range predicted by his FSIQ and GAI, and, actually, even his VCI, which is his highest index score. I don't see any evidence of a learning disability at this time, either.
But it is also not accurate to say that his skills are not significantly above grade level. Written expression and math fluency are both notably gated by fine-motor skills; if his handwriting development is merely age-appropriate, it would not be surprising for those scores to be in the upper half of average, rather than above. You also note that the higher level reading and math reasoning skills are his strength areas. It is possible that his teacher is assessing his achievement level by his written output, which may not be (probably is not) fully representative of his academic skills. Math scores in that range are well above grade level, not just a little above, and if his reading comprehension is in the same range, the same would be true there. It is also possible that you have a particularly high-achieving school community, in which case the teacher's perspective may be locally accurate without being consistent with national normative data. (IOW, just a little above grade level for your community, although well above grade level when compared to the nation-wide population of age-peers.)
His working memory and processing speed are comfortably in the range often observed in GT learners--high average, but not at the same level as his reasoning. This is not surprising, as, in addition to age-appropriate fine-motor skills, GT learners often also have age-appropriate executive functions, manifesting here as working memory. And yes, fluency and processing speed are closely related.
The questions of choosing more challenging work, and advocating for more challenge, require a better understanding of what "challenge" looks like in his setting. If "more challenging work" is just the same level of complexity of work, but more of it, then there is no particular reason he would seek out "challenge" in his setting. Sometimes the absence of significant complexity is not apparent to teachers. For example, say he is expected to do single digit addition and subtraction, but he's already mastered them. His teacher may believe that giving him double- or triple-digit addition and subtraction is "more challenge", but really, what he needs is multiplication and division. More digits of the same addition and subtraction is not increased level of complexity; it's just more volume of the same type of work. So when he "chooses" not to do "more challenge", the teacher perceives that he's been offered more and won't do it, and sees no need to increase the level of complexity.
