i am not a terrific kayaker, have only done it a few times. i do not know who does kayak trips to the reef. here is what i do know:
journeys end resort, on the north end of the island, does (or used to anyway) kayak trips thru the mangroves, and rents kayaks to go out to a bouy. there is a big rock with some coral & fishes around it. you just hop out & snorkel. it was maybe 20 minutes out there. the kayaks are free to guests of JER. get their website from the home page.
i have a few photos at: //ambergriscaye.com/jane