I've skimmed through the thread, apologies if I'm repeating others too much.
I have the 500L II, the 1.4x III, the 2x II and the 2x III. I've used all combinations extensively.
I agree with the general sentiment that the 1.4x is better. It does not degrade image quality to any appreciable degree, and the combination functions as a solid 700mm lens. Autofocus may be slightly impaired, but not to any extent that I've noticed before.
Using a 2x extender does soften the image, and add some colour fringing. BUT it is by no means a deal breaker - you can get excellent images with this combination. It doesn't feel like one lens unit though, you can really tell there's something in between the lens and the camera. Autofocus is much slower, and you are restricted to the central focus points on those cameras that do autofocus at f/8 (except the 1Dx II?). Note one major difference between the two extenders - should you be interested in birds in flight, the 1.4x is usable, the 2x mostly not for this. However, as someone else said, you get more detail with the 2x than you would by digitally enlarging an image taken with the bare lens or 1.4x, so it can be worth it for smaller/more distant subjects. In fact I use the 500+2x III most commonly of all now.
I would recommend to anyone doing this to stop down the aperture slightly. I use f/10. It regains a little of the sharpness that is lost by adding the extender. There is no need to stop down with the 1.4x.
Oh and fwiw it is my understanding and experience that the mark II extenders are not optically worse than the mark IIIs, just that the newer version works better (for autofocus?) with the latest supertelephoto lenses.
If you want examples, here's a gallery of images taken with the 2x III: https://flic.kr/s/aHsjWv9M6b