Ok, I've checked all users remaining in the list targeted by the new system and I've decided to speed up the events a little bit (as I don't see a decline in cheating despite all my announcements).
Anti-cheat system is now running in full-auto mode, which means you will only get one warning and a permanent ban afterwards in case of repeat GPS falsification.
Obviously, if the system makes a mistake and accidentally punishes a genuine player I will be happy to review that case and unban the wrongly accused party.
However, as stated in the original post, any attempts at deception and time wasting will not be tolerated and may increase your punishment to include the entire device (not just one account).