Maybe known, but anyway.
A Kenko 1.4 PRO 300 DG won't do the trick on my 7D with 400 5.6. I guess you need a DGX .
Just had a look on the Kenko site. It should not be possible according to them. They state that:
"Most Canon EOS camera bodies are programmed to shut down auto focus if the calculated effective aperture for the lens and teleconverter is smaller than f/5.6, the Kenko Teleplus PRO 300 converters work the same way"
Childeric, Not to be a pain but that is not exactly what you wrote. In fact, what you wrote is not at all what I wrote .