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Here's a thought. Use a four-sided die for ranks and an eight-sided die for files. This would only swap pieces on the same side. You can have an additional King safety rule, such that no King may be placed in check by the role of the dice. It could work in one of two ways. (1) The dice are rolled over until the resulting swap will not put a King in check, or (2) the results of the dice are ignored when the swap would put a King in check.