I think that the approach that the psychologist suggested is the appropriate one: tie your requests for modifications and accommodations directly to his diagnoses.
You could suggest something like for a 504:
Because student frequently becomes anxious when work is significantly below his intellectual level*, and this anxiety interferes with his ability to meaningfully access or benefit from instruction, teachers should give student work commensurate with his intellectual ability in order to reduce his classroom anxiety and allow him to focus on the material being taught, enabling him to derive educational benefit from the educational experiences being offered. "Commensurate with student's intellectual ability" is defined as being at a level consistent with student's performance on (testing instrument you want them to use).
Because student finds it difficult to sustain attention on work where he has already mastered most of the content,and this interferes with his ability to access the curriculum, student should be allowed to pre-test out of topics where he is already at 80% mastery and advance to areas where he is learning predominantly new material in order increase his ability to sustain attention and benefit from instruction.
Set up a similar cause-and-effect statement for every accommodation and modification that you are requesting, including extra time, quiet testing conditions, etc. Include defining measurements or criteria wherever feasible, so that the school can't claim they are accommodating him (for example, by giving him more of the same, instead of advanced work) when they really aren't.
* If the school wants something to back up the nexus between the disability and the accommodation being requested, you could include something in this instance like "often believing that he must misunderstand what is being asked of him, or believing that his teachers perceive him as being less capable than he is," in this. Ask your psychologist for further suggestions.
