Let us focus on the auxiliary have. Would it make antecedent time extents altogether? Antecedent time extents always would be relative to the head time. To shape up a good idea for head verbs and time, we can venture common sense, as also in literature. The common sense truth here is that it can take real time to make hypotheses, but hypothetical time could never be the same as real time.
Past form of the Modal MAY.