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grenv: I think that the crux of our disagreement is this: when does a test for mate occur? I contend that a move that would--in a given position--suffice to produce mate on any move numbered 21 through 39, would also produce mate on move 40.
I think the move 40 sequence is: (1) black plays a move, (2) one tests for mate, (3) if not mate, an ice age occurs, (4) one tests for frozen king(s). I think your move 40 sequence is: (1) black plays a move, (2) an ice age occurs, (3) one tests for mate or frozen kings.
In your sequence only, it has become simultaneously possible for the white king to be mated and for the black king to be frozen--yet another situation not mentioned in the game description at chessvariants.org