I keep my HDR settings as AEB in C3 with no issues. I just set my AEB for a 7 shot burst, p. 315, then saved that to C3. You can't save the IMHO worthless in-camera "HDR Mode" setting to the Custom Shooting Modes.
Thanks for your feedback.
Certainly an HDR image can be made in post-processing from single exposures taken using AEB, and these setting can be stored in Custom Shooting Modes.
The point of my question was how (if even possible) do you store HDR Mode settings as a Custom Shooting Mode. It doesn't appear that this is possible, although I can't see why it wouldn't be feasible - whether or not it is judged a worthwhile camera feature.
For me the advantage of the Custom Shooting Mode is the ability to quickly compose a shot where all the camera settings have been thought out in advance.
When I have used the HDR Mode in the 5D MkIII, I save the individual (RAW) images, plus the resulting HDR (JPG) image. I can quickly get a sense of how effective the HDR process was for my subject, while giving me the freedom to use the individual images later in post-processing.