Ah, my dd's bd is just a bit after that and she was able to start K shortly before she turned 5 so she was already one of the youngest. She is not a DYS level kid. If yours is DYS and already on the older end, I see why you would want him up two grade levels. Up one grade level would put him where my dd already was pre-skip and that was insufficient for her. I imagine that that would be insufficient for your ds as well, then.
We've been pretty good with a single grade skip for a few reasons. One, she was already young like I mentioned so she is quite a bit younger (up to 2 yrs). Two, she skipped 5th which put her into middle school and there seems to be more ability to differentiate in middle school b/c there are more kids and there is more moving around btwn classes happening already.
Would your school even be willing to consider a double grade skip or would they want to do it one year at a time? This was a long time ago, but my grandmother did it the one year at a time way. She skipped 3rd and went to 4th. The next year, she skipped 5th and went to 6th. Do you think something like that might work for him? It sounds like it might be harder socially for him to have to remake friends twice. Maybe if they could skip one grade and do subject acceleration in math again, he would have the chance to meet some kids in the next grade above that helping with the transition the next time he skips.