I think you got something there. Pictures of adam and eve after the fall show fig leafs covering their private areas. That would be some confirmation on the fall occurring from having sex outside each pair which caused the fall.The most probable candidate is dates, grows on a tree, and a darling of people of that region. Otherwise
Figs, Grapes, or Olives (common fruits if Iraq, if Eden was somewhere there). That also resolves the fig-leaf incident (it could not have been a leaf of the date-palm. Or did they weave date-palm leave stripes to make a skirt).