Is there not a symmetrical structure in the specific weeks and months given in the Flood narrative (Gen 7-8)?

Yes. As Wenham and others have pointed out, there is a symmetrical structure to the days and weeks described in the Flood narrative. That is, matching 7 days of waiting for the Flood (Gen 7:4) were 7 days of waiting for the dove to return (when it did not); similarly, 7 more days of waiting (Gen 7:10) matched 7 days of waiting for the dove to return (when it did); there were 40 days of heavy rain and flooding, and 40 days between the landing of the ark and opening of the window; and there were 150 days of flooding and 150 days of ebbing.