For what it's worth... if F4 isn't enough to stop action, F2.8 likely wont either,
Huh? Then why do lens companies spend the extra R&D money developing lenses an entire stop faster?
OP: For $1200, you should be able to get the 135 f/2 L as well as a 50mm f/1.4. Those two lenses would go a long ways in shooting the events you described.
Exactly. 95% of my sports photos are at f/2.8. I wouldn't shoot at f/4 indoors; that's an entire stop of light!