Thrown Rings should cancel each other out in midair, turn into golden Rings, and bounce back the way they came.
This would make for neat tactics like using Automatic Rings as a shield to protect your team in CTF.
Homing Rings are underused, so you could power them up a bit by having Homing Rings be the only thrown Rings to not be cancelled by other Rings.
Console variable?
I just had this image of two people with Automatic standing at such a distance that when they both fire, the Rings bounce back and are recollected by them.
So maybe the Rings could just bounce in a random direction.