Sorry to quote this pic again but I'm in the market for some bullhorns with a short reach and intern cabling - a bit like like what she's using.
Although it isn't clear from the picture, I don't think they actually have a short reach, they are V-shaped across the width, so the handles are actually well forward of the quill. But to answer your question, the Syntace Stratos sweeps back slightly from the centre, so it probably has the shortest reach of any bullhorn. Cables go through the bar up to the corner, not all the way to the centre bulge.
Although it isn't clear from the picture, I don't think they actually have a short reach, they are V-shaped across the width, so the handles are actually well forward of the quill. But to answer your question, the Syntace Stratos sweeps back slightly from the centre, so it probably has the shortest reach of any bullhorn. Cables go through the bar up to the corner, not all the way to the centre bulge.