I have the 70-300L and a 5DIII. I purchased a Kenko PRO 300 AF DGX 1.4X on ebay and tried it for a few weeks. Overall, IQ was pretty good. It was definitely better than cropping. However, as others have mentioned, AF hunts quite a bit, particularly in low light.
I should mention that my unit was an older version. Apparently, the newer versions have a green or blue dot on them and have newer firmware that fixes some of the AF issues with certain lenses.
I ended up returning the Kenko and purchasing a used T2i body, which gives me 1.6x reach and better AF with the 70-300 (when compared to the Kenko+5DIII).