Well, the in-camera HDR is really a gimmick for casual users. It's JPEG only, and the HDR options are limited. For the in-camera HDR, it can only burst 3 exposures +/- 3EV. For normal AEB, it allows up to 7 exposures, also +/- 3EV.
So the HDR function is just a subset of AEB, since it still saves the 3 raw files (if you keep the default options). You could just as easily do a 3 exposure AEB instead of using HDR.
Since you shoot HDR so much, you really shouldn't consider the built-in HDR on the 5D3. I'm sure that you'd be disappointed by it. It's interesting, but not a serious attempt at good, professional HDR. As you suspected, the AEB is really what you need, but since it's limited to +/- 3EV, you'll probably still end up doing manual bracketing, so that you can go well beyond 3EV.
I'm not sure why they limit it, since theoretically the camera should be able to automatically go up and down with the exposure as much as you want.
I shoot HDR using the Promote Control unit you mention, and I find it very effective. I find HDR is best done shooting manually via the camera mini-USB port, varying only shutter speed and taking all the images without touching the camera. As you mention it is possible to bracket a very large range of exposures - but not exceeding 30 sec.
The AEB on the 5D3 allows up to 7 images, and this usually covers needed range for most HDR situations. I process these in post using Photomatix.
I too wish that the HDR option built into the 5D3 had more options, mostly more than a 3-image bracket range.