I don't shoot macro and I don't have a macro flash, but the little I know about lighting suggests to me that in order to stop the reflections from the ringlight from looking like a ringlight you need to stop the lighting from looking like it comes from a ringlight.
Think about how light is reflected in people's eyeballs for portrait shots, or in sunglasses. The reflection you see is very much exactly as the light source was, whether it's a flash, a softbox, the sky, a ringflash or anything else. Here are a couple of examples....
Here the lighting was from a flash into a reflective brolly. You can clearly see the illuminated spokes from the umbrella reflected in the eye and the frame of the glasses.
Here you can plainly see the reflection of someone holding a reflector and you can make out the shapes very clearly.
If the problem you have with the light from your macro flash is that it looks like a ring (with breaks in it) then you need to stop it looking like a ring. A far more natural looking appearance would be an even, round, disc of light, which will look like the sun, a squareish light that looks more like light from a window, or a simply huge (relatively speaking) light, just like open sky (without direct sun). To achieve that you're basically going to want a softbox of some description, and to get the lighting off the camera, or at least off axis. That should also add a little shape to your subject as the directional light will allow the formation of soft shadows, visible from the camera viewpoint.
In nature it is rare for light sources to originate directly from the observer's own view point. I think a more conventionally shaped light source, positioned in a more conventional place is probably going to get you the results you seek. As has already been said, the ringlight should be fine for the times when you are shooting a non shiny subject. For other times you might need a different type of lighting. A small softbox - maybe 8"x8" or 12"x12" - fitted to a 580EX, or a flash fired into a reflector (sheet of white card should do) should produce a wonderfully soft, wraparound light for a small subject, and remove those hotspots and odd reflections.
Still, that's the theory (well, my theory). I'm sure the macro experts will be able to advise you better. Good luck.
