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DRC TOLERANCE FACTOR applies globally, so it can't be applied to just one rule. You might have to consider modifying the rule itself, or creating a modified copy of the rule, or making a separate run with DRC TOLERANCE FACTOR and just that one rule selected with DRC SELECT CHECK.
If you oversized the smaller shape by the same amount as the desired overlap, and then performed XOR between the larger shape and the oversized shape, what would the slivers (false errors) look like near those angled edges? I wonder if they would be something that could be filtered out with another operation, without compromising the integrity of the check for the non-angled edges.