You and me both mate! I'm still figuring out the 5D3 autofocus myself. I managed to get maybe a 20% hit rate the first time I tried tracking my Border Collies chasing a ball (if there's ever an erratic subject, that is it) so definitely some learning to do. I haven't even had a chance to read the manual yet though as work is pretty well consuming me at the moment.
If I do have some success I'll post my findings here.
One thing that works REALLY well for birds etc against just the clear sky as a background is using all 61 AF points and letting the camera decide which to use when a subject enters the frame. I was mucking around the other evening in low light tracking fruit bats as they flew over my house and I was really impressed. Wouldn't help much in your situation though as there'd be too many distractions in the background.