Thanks, guys - it looks like some of my suspicions were well-founded. I certainly don't want to be standing around Jamaica station wondering if the bus is ever going to show up and worrying that I have a flight to catch and zero other options if I miss it. Perhaps when I return to JFK I will see if the bus to Jamaica is around...
On a related note, if the JFK-Jamaica bus is really the JFK-LGA bus with an added stop in between, it beats me why they can't offer the Jamaica option on their Web site.