Widely used personal wallets with built in p2p mixers should have plenty of clean money and people mixing. If mixing is legit, I don't see why that wouldn't happen - everyone wants privacy if the cost is low.

Maybe people wouldn't cooperate for no reward as you say. So do you think a reward-based scheme might work? Remember that with the MPC algorithm the authority won't actually learn anything about you, only about the victim of the trace.