I think the main thing to play with and adjust would be the angle of the cones sides.
Intuition would suggest a 45 degree angle with the horizon, but that may not be the case. I have seen cones with straight sides with angles from 30 to 70 degrees of axis.
As far as size, the cone in the picture is the largest I have ever seen in relation to the driver it is above. The main thing I see is that the cones are generally the same size or larger than the source of sound. (excluding the cones with steeper angles, the cone would have to be very large) SO in the HWK case, the size of the top port or larger.
Also, the cones are often not even straight, they curve inward. )(<----cut right there.
here are some pics of professional speakers:
http://www.cd-konzert.com/loudspeaker.htmhttp://www.bolzano-villetri.com/both are omnidirectional high end speakers, but give you an idea of what kind of things can be done to convert vertical soure to horizontal.