I now use the Canon 2x III on a Canon 70-200 f2.8 IS II, and I am very pleased with the match.
The Canon 2x III doesn't show the ugly OOF-artifacts I observed on the 1.4x II.
I am glad that combination has worked for you. I'll share a different experience.
I tried the 7D / 70-200 f2.8 IS II / 2X III combination. Intitial shots showed severe Front Focus Issues. I talked to the folks at CPS about the setup asking if Microadjustment settings would remember the combination as its own lens, or would it also apply those microadjustments to the 70-200 by its self also. They could not answer that question, so I exchanged that extender for another. I later discovered that the combination is remembered as it's own lens.
Based on the intial bad results with the replacement extender (and really wanting that combination to work for me) I tackled lens Microadjustment. What I discovered was that at 400mm, the setup was fairly accurate, (although also somewhat inconsistant) with little or no adjustement needed, but at 200mm I needed to adjust focusing to +12 on the -20 to +20 scale. I decided this was not going to work for me, so I returned the second extender.
I understand that lenses and extenders are built to tolerance ranges, and if the tolerances of the lens and extender are at the oposite ends of that range, problems could result. CPS suggested I borrow one of their 2x's to compare, as the ones I purchased may have be built together with similar tolernces towards one end of the scale. I have not tried that yet. I may give the 1.4x a shot but I really wanted to get to 400mm.