Honestly, unless this is paid work at pretty good rates, either the $11K EF 200-400mm f/4 Ext. 1.4X or the $9K EF 500mm f/4 are probably overkill. You can get pretty close in terms of IQ with an EF 100-400mm f/4.5-5.6 L IS II for about one-fifth the price of either of the other lenses. You'll also get very close to the IQ of the 100-400mm "II" using an EF 2X III extender on an EF 70-200mm f/2.8 L IS II.
Other, more affordable options are:
- Sigma's 120-300mm f/2.8 DG OS HSM Sport. It's a fairly good lens and costs 1/3 the price of the 200-400mm f/4.
- EF 100-400mm f/4.5-5.6 L IS II.
- One of the Sigma or Tamron 150-600mm f/5-6.3 offerings. They're not quite as good in terms of IQ, but they are "good enough" for a lot of shooters.
- EF 1.4X III and EF 2X III with your existing EF 70-200mm f/2.8 L IS II
Any of the solutions you suggest should be adequate to do what you want at a fairly high level. Which option is best for you is more of a personal preference based on how much you're willing to spend for angle of view flexibility and that last tad of image quality.
If you already have the EF 70-200mm f/2.8 L IS II: one option is to add an EF 2X III. The 70-200mm f/2.8 "II" is about the only zoom I would consider using a 2X with for action/sports, but it takes the EF 2X III very well and still focuses reasonably fast. That would give you a 140-400mm f/5.6 which should give your 5D Mark IV no trouble autofocusing. The 6D might be more limited to using the center AF point only.
The EF 200-400mm f/4 L IS with built-in 1.4X Extender gives you one nice advantage: you can engage and disengage the 1.4X extender without opening up your camera and lens to the elements. Adding or removing a lens or extender at the beach is particularly troublesome and should be avoided whenever possible. It's also a very flexible lens, going from 200-400mm f/4 to 280-560mm f/5.6 at the flick of a switch. It's also very expensive.
The EF 500mm f/4 gives you a wider maximum aperture at 500mm than the 200-400mm 1.4X does. It doesn't give you much flexibility in terms of framing, though. It is about 20% cheaper than the 200-400mm 1.4X.
The 400mm f2.8 seems to be the lens for sports. However for indoor sports I use the 70-200 f2.8, but for outdoors and in particular for kitesurfing with reasonable light I wonder if that aperture is really a must.
It's not just about the aperture you're exposing with, it's also about the aperture of the lens wide open and how that affects the performance of your camera's AF system. The f/2.8 lens does open up more possibilities in that respect, even if you're exposing at f/4, f/5.6, or even narrower.
The other possibility for reach is getting a new body 7D mark ii (although it may be an overkill for camera bodies) to take advantage of the cropped sensor, but I fear I may lose out on IQ vs the FF that I could crop in post if need be.
If you're going to crop the FF camera anyway, the 7D Mark II will almost certainly give you better results in daylight conditions. I shoot with both a FF 5D Mark III and a 7D Mark II and there's not a lot of image quality difference in good light. The 7D Mark II is much better in that respect than the 7D was. The AF system of the 7D Mark II is also light years ahead of the original 7D's AF system. This is both in terms of configurability as well as overall accuracy and shot-to-shot consistency.
One thing to keep in mind with all of these options is the increase in shooting technique that will be required to get results anywhere near the capabilities of these lenses. At the magnification levels beyond about 300mm or so, every minute camera movement is going to affect the image. Even when shorter shutter times are used, it still takes about 1/300 second or so for the shutter curtains to transit the sensor as the slit between the first and second curtains moves across it. The extra size and weight of these lenses will also affect the ability to handhold them and get optimal results. A good, sturdy tripod with a high quality gimbal mount will probably be required for the differences between something like the 500/4 and the 100-400/4.5-5.6 to be noticeable.