Answering my own question here...
You can't compose the OK verb with any AsyncHandler like I'm trying to do (as far as I can tell), but you can get the job done by defining your own AsynchHandler implementation -- basically a replacement for the AsynchHandler returned by as.stream.Lines.apply().
See the source for dispatch.as.stream.Lines.apply(), which basically just returns an AsynchHandler that: (1) ignores the response status code; and (2) always produces a Unit response. Its a pretty simple thing to write your own version that actually does pay attention to the response status code, and throws an appropriate exception (such as dispatch.StatusCode) for non-2xx responses.
Brian Maso