I ordered a Soundlab SRC-144 DMX controller for comparison purposes. Unlike the Geni, the Soundlab's output *does* look like this website suggests it should and my PIC-based receiver circuit, programmed according to information from this site, *does* succeed in extracting sensible data from it, without modification to the code. So my project can go ahead and I conclude that the Geni DM-4 is NOT a true DMX controller despite what it claims.

I would still appreciate feedback from anyone else who's used a DM-4 though, as there remains the possibility that the particular unit I have, despite being brand new, is in some way knackered...