I have been able to successfully use my Kenko 1.4X Teleplus Pro 300 converter with my 5D Mark III. I have had no problems at all using it with my 70-300 L, which by the way does autofocus when the Kenko is attached, even when it is at 300 mm, which theoretically it shouldn't as the max aperture is f5.6 at that point, so with the 1.4X, I'm at f8.0. Data is reported in EXIF file correctly as the 70-300 lens and it shows 420 mm as the focal length. I also have tried the Kenko with my Sigma 150 Macro and the 24-105 kit lens that came with the 5D Mark III, and both also seem to work fine. I just bought the Kenko from Adorama about 6 weeks or so ago, so maybe they changed something in it that is allowing a newer version to work? The Kenko also works fine on my T2i, also allowing autofocus on my 70-300 when its at 300.
I've attached a shot taken tonight with the 70-300L @ 300mm with the Kenko 1.4X. This was handheld at f8.0, 1/500 sec. ISO set to 3200. One of the main reasons I wanted to get the Mark III vs my old T2i was the ability to use the higher ISO, both for faster shutter speeds to help in windy conditions and/or low light like this picture which was taken in total shade. These are jpgs out of LR4.1, absolutely no noise reduction added, so you can see how little noise there is at 3200 ISO. First one is the full frame, then cropped to just the tulip.
(I haven't posted pictures before, so hopefully these will show up. When I did the preview before submitting,I am not seeing the pictures, but it shows them to be attached.)