Okay just went off and looked at a picture of a k4.
I think that a more simple method will probably rear it's head if you hunt about.
The < and > buttons must surely be mappable to keycodes that the app would expect.
Where does it dump those events, IS IT THE SAME PLACE AS THE FIVEWAY? if not it's probably not working because it's only servicing one event folder. at that point I would attempt to make the Click of the 5 way the right event(that would be my first thought)
IF IT IS in the same events location: I would tweak those codes to be the same as the output of the z on 3 and see what happens. perhaps we could find out what that is. That would probably help.