finca, you present a fairly consistent picture that suggests your verbally gifted DC may also have a specific learning disability in math (although many districts and some professionals would not choose this classification, since it appears the absolute level of math skill is actually at least average). Your DC's self-perception has some validity within the context of personal experience, even if not in comparison with the general population.
Although the profile is weaker in visual spatial skills across the board, it is also quite strong in nonverbal reasoning, which is likely going to be the avenue to compensatory strategies. I also note that fine motor speed appears to be particularly slow (Coding). Without having observed test-taking behaviors or asked further questions during testing, it's not clear what's behind that, but I'll throw a few possibilities out, and you can think about which ones seem to fit your observations best: fine motor coordination, visual memory, nearpoint copying (which involves having to look up and down quickly without losing track of where one is in either location--typically has some relationship to visual tracking). There's data to support visual memory as a significant factor (PS), but there may be other factors in addition.
Given the auditory working memory strengths and the visual relative weaknesses, it is not altogether surprising that math facts are solid but math reasoning and number sense are not. Math facts, in any case, are to some extent more akin to learning vocabulary than to true quantitative concepts.
If we wanted to discuss a diagnosis, one of the constructs (not a DSM Dx) that might be of value would be nonverbal learning disability, with the caveat that his extremely strong fluid reasoning/nonverbal reasoning skills may or may not always be found in those who fit the profile.
But more importantly, some suggestions for compensatory strategies include:
1. Use language and abstract reasoning strengths to support visual spatial weaknesses. For example, step-by-step verbal explanations will probably make more sense than a worked problem without consistent accompanying language.
2. Explicitly teach problem-solving heuristics, for example, this nicely-curated list taken from the Singapore math syllabus:
https://seriouslyaddictivemaths.com.sg/what-are-heuristics/or this more-official, but less approachable listing, with instructions for how each problem solving approach works:
https://repository.nie.edu.sg/bitstream/10497/2928/1/CRP1_04JH_Conf05%28MES%29_Tiong.pdf
3. Reduce visual clutter. Not only limiting the number of items on a given page, and making sure there's plenty of white space around each one, but also better defining the visual space, such as by dividing a page up into large rectangles (in a grid), with one problem in each.
4. Aids to visual organization. These may include tools as basic as working all problems on grid paper, to reduce misaligned calculations. Some students benefit from using a couple of colors of highlighters, and going through problems before beginning them, highlighting either key words that will help them figure out what math to do in the word problem, or signs and operations, to make sure they compute correctly with them.
4.a. Flowcharts for problem solving. This could be listed under heuristics too. It's also not always effective with this profile, but might still be worth a try.
5. Teach math in as rich a real-world functional context as possible, preferably with applications to something personally meaningful and relevant. With these strong fluid reasoning abilities, once your DC understands the "why", there will be more tools to support the visual spatial relative weaknesses.
BTW, the testing suggests that your DC's underlying quantitative reasoning skills (in some areas) are actually quite high, with one of the best subtests one that has a fair amount of relationship to algebraic thinking (Figure Weights), which suggests that there should be a path forward to feeling like a much more successful math student. Geometry and physics, OTOH, may be a different story.
