When players who were banned for cheating are let back into either of the competition-running lobbies, they should undergo a probationary period during which they lose privacy rights for all accounts, be they linked alts or clean-slate mains. The mods can set up a thread with a list of all accounts held by recently unbanned cheaters and either (a) consistently monitor users who have made the list or (b) install a simple account approval process whereby failure to inform the mods of newly registered accounts constitutes a violation of the rules.
This might be worth a go for any game-related ban, not just cheating, but that would probably involve a lot more maintenance.