The new 2X Mark III Extender with the new 70-200/2.8 IS Mark II is supposed to be pretty good. I haven't tried it, though, so this isn't from personal experience.
I'd still suggest get the 400/5.6, though... It will likely be better image quality. You'll probably want a monopod or tripod, though.
A 300mm lens, by itself, will generally not be long enough for a lot of surfing shots. On the other hand, the 300/2.8 works very well with both 1.4X and 2X Extenders (even Mark II versions, which can be bought a lot cheaper than the Mark IIIs).
An interesting alternative might be a Sigma 150-500 OS. It's an f4.5 to f6.5, if memory serves.... But most surf shots are done in elatively bright light. I think it's about $1000 US lens.