Re: Accounts
This is the flaw: "he may be a mild cheater, or just an unlucky player."
We know that on average fair players don't cheat. We also know that cheaters cheat more or less. Since we can't identify cheater with current architecture, that means that the score will represent not the cheat-attempts count, but a "was seen around a cheater" count. Now we can't base any sort of ban actions around that.
Comparing the "was seen around a cheater" count of the average player, which we can assume to not be a cheater, with that of any player can be safely used as statistical evidence for that player's honesty evaluation - the larger the difference, the more often and the more likely is that player to have cheated.