usually larger apertures are made for shooting in low light situations....that way it lets in more light for any given shutter speed....i would think at the beach you would have enough light at F4 or even smaller to get your shutter speed fast enough to catch all the action...
the reason why your lens is fuzzy it just because of the quality of the glass...which is the main reason the 70-200 L glass is so expensive because at either F2.8 or F4 it is gonna be sharp...
F2.8 is gonna make it have a pretty shallow depth of field where on a surfing shot i would want the whole wave to be in focus so i would probably use F4-F10 depending on what angle in comparison to the wave i was at....if you are dead on a larger aperture might work...but at an angle i would use a smaller aperture to get it all in focus...
the reason why i want F2.8 is because i plan on using the lens inside sometimes and want some more light without having to use a tripod...