My Kenko DGX PRO 300 causes my 5DIII to lock up when used with most of my lenses lenses, including the two that I mainly wanted it for (the 100L and 70-300L). The camera is running the most recent firmware and the converter is also the most recent revision ('blue dot'). Once locked up, you have to remove the camera's battery, and you loose the last shot image.
When I first got my 5D III, I was relieved to find that my DGX PRO 300 1.4X worked with the one lens I needed it for (the EF300 f/4L), having read various, somewhat confusing accounts of the difficulties others were having.
A few weeks ago, after not using the combination for some time, I put the lens and TC on the camera and encountered the lockup problem. I soon resigned myself to the idea that I might have to spend for a Canon TC.
Eventually, though, I did remember one thing that had changed since the last time I used them: I had fooled around with microadjusting my 40mm f/2.8 pancake. The following is what I think allows me to get the TC working again: With the 40mm on the camera, I disable the AFMA, AND
I shoot a frame with the new setting (disabled AFMA). Then I turn off the camera and switch to the lens with the TC.
Bear in mind that I have just one lens microadjusted, so I have no idea how having multiple lenses AFMAed would complicate things.