How about testing focus with the 135 f/2L (with the 1DxII) ? It is cheaper and lighter than a 70-200 2.8L IS II
Here's what I found in the manual, I've read it through before, that's why I was puzzled by the 3 fps,
"With Servo AF shooting:
When [AF operation] is set to [Servo AF], the continuous
shooting speed of max. approx. 5.0 shots/sec. will be given priority."