Welcome!

FWIW, his PSAT 8/9 scores would appear to be in the college-ready range (although one should interpret these with some caution, since they are likely to be in the range where ceiling effects increase the error), and do support the conclusion that he picked up a lot of math skills last year in algebra I. Did he take the PSATs with accommodations?

My main question with respect to skipping eighth grade would be whether his writing skills are actually high school-ready. He's already demonstrated HS-readiness in math, by completing algebra I successfully. The other measures reported are from group standardized testing with limited written expression demands (mostly computer-administered or bubble/grid-in), which don't document writing skills in a naturalistic context. The only data of that nature we have to work with at this moment is your reports that he may have an undefined written expression disability--in which case what you are trying to document is that he is specifically -not- high-school-ready (or even grade-appropriate) in writing. Which would tend to be a counter-argument to another full acceleration. If, instead, the outcome of your current eval process is something along the lines of modifying his 504 to support AT for writing (but without need for specialized instruction/remediation), then the acceleration prospects become more positive.

TBH, if he is found eligible under SLD-written expression, I think it would not be in his best interest to do a full grade skip. If AT accommodations resolve his written expression gaps entirely, then he doesn't need an IEP, and should remain on a 504 with updated accommodations.

This is all regarding "can". Should he? That's a much more nuanced discussion. I do like starting from what the student wants. He's bringing it up, so it's definitely worth a thoughtful and patient conversation about what problem with his current educational situation he is trying to solve, why he thinks this is the best solution, what possible new problems the solution may create, and how he or his team can address those possible new problems.