They deliberately attract those "in it for the money" by huge cash reward (while biasing the audience to those impressed by money),
Randi has stated that if someone does win the money, they can designate a charity to recieve it instead. He explicitly made this offer to Sylvia Browne when she backed out of the challenge, after saying she would accept it, by saying that she's not in it for the money (despite all evidence to the contrary).
seem to filter to select a high number of high profile fraudsters
How does he know the fakes from the "real" psychics before he tests them? He only makes an explicit offer to high profile people like Sylvia Brown and John Edward, but anyone is free to contact him if they think they can prove their claims.
choose their own tests rather than involving independent third parties.
The exact nature of each test is proposed ahead of time to each claimant. The test doesn't go forward until there is complete agreement on both sides. This is to prevent an exposed psychic from saying things like "these lights were interfering". If the lights are going to interfere with your gift then you have the chance to have them switched out with lights that won't.