Hi KJP,
Here are some that I've bookmarked, based on where we can reasonably travel to for drop-off/pickup: Camp Starfish, in New Hampshire; Camp Akeela in Vermont; Franklin Academy Summer program in Connecticut; Talisman Camp in North Carolina; SOAR in North Carolina. I've seen others listed in other parts of the country too.
These all promote themselves as integrating explicit social skills training into the regular day of camp activities, with an emphasis on helping kids internalize the strategies. I think the challenge with the school social group is that it is removed from the action. It provides a safe space to discuss things, but usually the moment of interaction is long gone.