Have you considered drilling the rivet out?
That's what I usually have to do to remove a rivet. Be sure to use a drill press or it might slip.
After drilling it out, you could tap the holes and fill them with small machine screws - maybe a brass screw for contrast. Use a screw that has an allen wrench hole or phillips rather than a flat head. The allen head screws are usually flat black and might look good as-is.
Another idea is to use a brass or stainless steel pin that fits in the hole. Make the pins a little long so that they will stand proud of the surface. Then round off and polish the pins with a buffer and polishing rouge. This could really look cool! If the drill holes are just right, you can press-fit the pins. If the holes are slightly too big, you could use Loctite or epoxy to hold them in.
Chuck