My son has a similar profile to your son (with the VCI and PRI reversed).
We homeschooled K-4 and then my son entered a small private school the next year in 6th grade (skipping 5th). He skipped 7th and is currently in 8th. He is further accelerated in math (one year ahead of his current placement).
Because of his processing speed issues, he has accommodations at school where he is allowed double time on tests, but he rarely uses it.
Honestly, from a cognitive demand standpoint, two skips haven't been enough, but from an executive functioning perspective, it is bordering on too much. Since we don't want him to burn out before he even starts high school, we have decided to have him take a gap year (or two) before entering 9th grade. We'll be homeschooling again. I hope to work on skills that have been difficult for him and at the same time stretch him intellectually--something that's been lacking for the last two years.
This is about what our situation has been with our DD14, too. She's now (finally) catching up to peers in EF (that is, 17yo, not agemates) and surpassing them, even... but we were pretty nervous about this heading into her senior year, to be honest.
The way that we did this is as follows:
delayed entry into formal school until 6.5yo-- and at that point, provided out of level testing that was all 99's, arguing for a 3rd grade placement (that's 2y right there, since she didn't turn 7 until the summer after she finished 3rd grade).
The FOLLOWING year, she compacted 4th and 5th into a single academic year, and the year after that, was placed as a 6th grader in the GT program.
The last skip was finalized when she was a high school freshman, and her grade placement was adjusted at the end of that year to be "11th grade" without ever having been 10th grade, if that makes sense.
What worked about this was that if her EF and written output
hadn't begun closing the gap in 9th grade (it had) we wouldn't have HAD to have her graduate this year-- we could have had her graduate at (almost) 16y instead, and just spend 5y taking "high school" coursework.
I can't say that the academics have been terribly meaningful, but some really good teachers can go a long way to helping your child find ways to enrich the curriculum as they go, provided that they are open and nurturing about that.
IMO, the
easiest way to advocate for a multiple skip like this is the way that we did it (and others here have done it, too); make sure that you're ENTERING a new educational setting, and that the child is
way over-prepared to be dropped into the incoming grade, convincingly so via test results, etc.
Homeschool to school is the simplest way of getting that done, because there isn't a "gap" for a school to really consider a "skip" in academics-- it's just that the placement is "individually determined" instead of "chronological."
I'll also add, though, that the processing speed would be a red flag for me here, too-- ouput demands REALLY increase sharply now at Gr 4, and again at Gr6/7 (the transition to middle school) and Gr9. Each of those particular years is a "transition" year where kids are specifically taught EF and academic support skills.
As far as we can tell, my DD's profile has
only her written expression as a limiting factor in the 3y acceleration that she's effectively been operating at since 6th grade-- but realize that as a 7th grader, she was clearly at about the 80th-90th percentile there as compared with her GT (mostly MG) classmates. It's only now that it's bounced back up to 99 levels-- but like everything else about her, it's a total black box HOW that happens, and it's not been a slow steady improvement, either-- fits and starts. It's a step function, her development. {sigh}