I support suggestion A, but with some possible changes.
First, the bans will apply to both big and lite games - that is, if you commit a second offense, you are banned from the next three big games and the next three lite games.
Second, the counting of offenses will encompass both big and lite games - if you commit one in the big game, and another in another lite game, you will have a second offense, not two first offenses.
Third, that all Game Moderators - big and lite - must abide by the ban list.
Fourth, that "eternity" is defined as 30 big games and 80 lite games - that should be well more than a year. By that time, the player's desire for vengeance (if any) will be long gone, and hopefully they have matured somewhat and might able to be a contributive player. The exact number of games might need to be adjusted.