When shooting with speedlights into umbrellas (or umbrella products like the Westcott Apollo), vertical placement on a light stand has always seemed non-optimal to me. Two reasons: 1. This puts the light source away from the center of the modifier and 2. There is stress on the hotshoe, especially when daisy-chained (such as with a Pocket Wizard TT5) and tilted. I wanted to find a way to mount my speedlight horizontally in order to avoid both of these issues.
I looked around to see what was out there. I saw a number of DIY ideas and just one commercial product. I really didn't like any of them for various reasons. So-I created my own. In my opinion, it solves the issues involved with the other designs. It will fit any flash, is very secure, works at any angle, puts the flash head much closer to the umbrella shaft, and avoids strain on the hotshoes.
FWIW, I present my horizontal speedlight mount.