
Those help quite a bit to explain the extra outputs.
Ok, it looks like it's using a Schmidt Trigger to clean up the output, which inverts the signal. If my understanding is correct, the output from the chip is being fed back into one of the other I/Os to un-invert it and then again to invert it once more. The signal is brought out to the edge connector at each of the last two stages, so one is inverted and the other is not. I'm guessing they did this to make the board universal so that that it could be used with whatever hardware they decided to hook to it.
I used colors to show what each does. Blue and Green will connect to the data inputs. Dark colors are the inverted outputs, light are non-inverted. Try one set and if that doesn't work, try the other. Don't mix and match. Use either both darks or both lights. Red and Black should be +5v and Ground respectively.
Let me know how it goes.
RandyT