SnailZane, just to clarify: Neither of my suggestions take culture scores into consideration. If one does so, there is no way to not either punish or reward the one who resigns.
The first suggestion was to look at points (i.e. 3-0, 5-2-0, 6-3-1-0) from the games between the tied players. This only works if the match structures are symmetric, and it may not be enough to break ties. Especially for the current 2-player round robin structure). Games won would also not help, but would in the later stages.
The suggestion about looking at the 3-player game played between the players of a 3-way tie was specific to Intermezzo Championship where all combinations of three players play a game.
My wish (which is not specific to this tournament) is this: Please consider not us culture scores in tiebreakers since that may warp objectives of players and/or discourage resignation.