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I voted for keeping things as they are, but then I remembered about re116. Perhaps it should be limited; the option of subtracting a day after each such reset, i.e., 116-115-114, etc., looks good. Making the availability of a rematch after a game dependent on the position in the Global Order doesn't seem very logical, as there isn't a strict correlation between the position in the Global Order and the availability of an easy and quick path to an opponent.
As for 111+113, for me, this is the optimal compromise between not wanting to waste time and wanting to play full-fledged games.