Thanks for the ideas, everyone. And especially
Analise, who gave some sympathy and understands what I'm saying about the poor job they did telling the bus drivers where to take us.
There were no cabs around the Howard Beach station. I thought about calling one, but then the second bus showed up and I figured I'd be all right. In the future, I'll go through the Jamaica station via the E or LIRR...a couple people have suggested that. Though the A train to Howard was fast and problem-free...and included a couple of loud drunk frat boys for entertainment.
As for the flight actually leaving at 6:20, when I got to the checkin counter at 5:50, the agent told me "it is too late" to get on my flight because "they've closed boarding". Next time, I'd probably try to get to the Admirals Club and see what they could do. That hadn't occurred to me. At the time, I was just dripping with sweat from running around outside and rather tired from it all.