Ah, but remember, there were large open spaces in Lórien near the Anduin (remember where the Fellowship has a picnic with Galadriel and Celeborn before leaving?), so I'm sure there could have been other open spaces devoted to grain. And, of course, flour doesn't HAVE to be made from wheat. Nut flour often works just as well.
Though I still giggle at the Elf-in-overalls mental picture. Can't you just see one playnig the opening bars of "Dueling Banjos"?
