The systematic nature of sports shooting (speed, direction, depth of field, focus tracking, etc., etc.,)
means that no individual quality stands out, but one bad component brings it all down - theoretical
image quality is offset by speed of focus, anti vibration, and so on, ensures that your proposed system will
be impossible to beat by any bag of single fixed lenses. Don't underestimate how GOOD the AFS is, or how
effective a converter will be. No lens is SO PERFECTLY integrated with the F6.
When Sports Illustrated wants you to go shoot the World Cup, they'll pick up that 400/2.8 for you.
A 300/2.8 to shoot a pro striker wreaking havoc in the area is a lot of fun. But that's a Pro issue, and only if you are looking for a front page, above the fold shot. You won't be hanging 4 cameras with long fast primes on monopods over your shoulder. Do the 70-200.
You can ALWAYS rent a monster lens for that special event.
And you HAVE to show us the pictures.