It's pretty late in the year to try for a whole grade skip, but like the others I'd seriously consider it. Your situation sounds very similar to ours: dd14 has a late summer/early fall bd, barely made it by the K cut-off and we were told to hold her out a year due to intensity and sensitivity and age, and we have a pretty good high school that we've choiced her to with dual enrollment and a lot of other acceleration options. Middle school and elementary were also our problems.

We did start dd on time (shortly before she turned five for K) and she skipped 5th after we were told essentially the same thing you were: they were going to have a very hard time meeting her needs with a skip and an even harder time without it. She's headed into her junior year of high school now and it really was a good choice both socially and academically. She was still in the 99th percentile in most areas immediately post skip and remains there still.

Is it too late in the year to request that they consider placing him as a 6th grader next year?