I honestly think it should just be public knowledge that they have this special right, let all the figures and stats be published more regularly about their trades, and leave it up to the public to either punish them in elections, or follow them in their trades. Enforcement is useless because you only ever catch a small number (of those insider trader cases), but make it seem like the game is fair. Just tell everyone the game is rigged and play at your discretion knowing who the players are and what they are doing.
And you can bet their sudden change of heart on being for a ban on congressional stock trading is because they have set up back channels to do it by other means hidden from public view.