Simply give the players two 3 minute timeouts per match, to be used as they want....or one 3 and one 10 minute. If you can't get back on the court after 10 minutes due to an injury, you're done anyway.
That stops all the fake injury timeouts. You have the option of using your timeouts to take momentum away from your opponent, or hold them in reserve for an actual injury.
Huh? How does that stop faking? The option of using your timeouts to take away momentum is what we want stopped, not encouraged.