I know you've been on here for years (longer than I have!), but welcome, anyway!
You certainly do have a right to request an independent evaluation, if you are not satisfied with the results of this one, especially where you have data indicating that he has reading achievement that outperforms current assessments of cognitive ability, and which is inconsistent with past testing. To be fair, it is not totally illegitimate for the psych to interpret the decline as due to early instability of scores, but it's also worth noting that this is a very different instrument, with very different weighting of the various cognitive domains. In particular, the C/K score, which is the most akin to the WISC-IV VCI, is derived from a much smaller pool of verbal tasks, with more of a slant toward verbal knowledge than toward verbal reasoning, which is where (as you note) declines in an LD kid might be most notable. However, I should point out that those declines usually are most noticeable in learners with reading disabilities/dyslexia (SLD-reading, in educational parlance), rather than in those with math disabilities/dyscalculia (SLD-mathematics).
Anyway, the point is, this is not apples to apples. There are analogous measures, sure, but not identical. The places where the results are similar are in the clusters that are most comparable to the PRI and PSI. The WM-related score has gone up a little bit, the VCI-related score (as mentioned) has gone down quite a bit, and then an area that wasn't previously assessed on the WISC (auditory processing) shows up as relatively strong (this area is usually one of the contributors to predicting reading ability).
Secondly, (and possibly more importantly) even if one uses this set of data, one could make a fairly straightforward argument for SLD-math based on the unexpectedly low (and normatively quite low) math calculation skills. SLD-math calculation is a named disability category in the federal regs. The idea that average math problem solving rules out SLD-math is, shall we say, not widely accepted in the field. (On a side note, though, it is not unreasonable for a high school student who is effectively accessing grade-level curriculum without support beyond a calculator to be moved to a 504 with a calculator accommodation. This actually is an acknowledgement that the student has an LD, as the 504 would be based on the qualifying disability of SLD-math calculation. The distinction between an IEP for SLD-math and a 504 for the same SLD is the presence or absence of a need for specialized instruction.)
"Sec. 300.8 (c) (10)
Statute/Regs Main » Regulations » Part B » Subpart A » Section 300.8 » c » 1
(10) Specific learning disability—
(i) General. Specific learning disability means a disorder in one or more of the basic psychological processes involved in understanding or in using language, spoken or written, that may manifest itself in the imperfect ability to listen, think, speak, read, write, spell, or to do mathematical calculations, including conditions such as perceptual disabilities, brain injury, minimal brain dysfunction, dyslexia, and developmental aphasia."
This is well low enough to apply for a calculator accommodation for the SATs, too, btw.
Another model for SLD diagnosis involves unusual intra-individual differences. Given that the entire assessment (cognitive and achievement) appears to have employed the WJIV, they should be able to generate data on the significance and rarity of his magnitude of diversity of cognitive and academic skills. What model of SLD pertains to your situation depends on your local and state regs,
Outside of formal testing numbers, how is his actual school experience?
