This can be counteracted by broadcasting with a delay, something I believe they already do. It may be the case that the delay needs to be increased.

Chess turns can take 20+ minutes sometimes depending on the time limit of the game, so that would be quite a delay, and then you would still have a problem with a live audience.

How about a 'turn-delay'... the broadcast field is always three turns delayed rather than a static time delay

Well if there's 3 rapid fire exchanges (trading Queens & Rooks for example) lasting 10 seconds total, followed by a 20 min move, then the broadcast would have to freeze frame on the 1st move in the rapid fire sequence, so as to stay 3 moves behind, with the last 2 "hidden" moves evident to all that the pieces will be traded.

Then you again require communication to the players, which a Faraday cage would solve.