My statement was a bit off. The race condition is not inside MHD_epoll() and its cousins, but in the loop surrounding them. So I get an incessant series of calls to e.g., MHD_epoll() at a very high rate, without anything actually happening. I have landed inside MHD_accept_connection(), and as you suggest, the problem probably resides somewhere in that routine.
For some reason, the examples are not built on my system, although I haven't switched them off through configure. Could be the bitbake build environment, but I'm not sure.
For now, I'm not too worried about that.
I just tried the MHD_USE_AUTO etc., it makes no difference.
Will keep on digging in MHD_accept_connection(). It returns 0 on its very first call. Not good. I have a feeling that I'm getting closer.