I think you're exactly right. He's DEFINITELY playing with me, because he "challenges" me before and after the biting, like, "come on Mama, let's wrestle!" He spent a lot of time with other puppies before we brought him home, so he's used to tumbling and wrestling (and, of course, biting). I know he needs to play-bite to learn to temper the strength of his bite as he grows up, but it's sort of painful for me.
When I shout "No!" at him, he barks at me, as if my "no" is a people-bark and he's just answering me. So I think the key is to teach him to play with me in other ways.
I just don't want to hurt him.