Both.
I definitely think you should write out some of the stories (especially if you need the words for the count 

 ).  Anything that helps us empathize with and understand Hadwin as a character is good, as well as anything that helps explain your allegory of "God" in this world.  However, if Hadwin is sharing a lot of these stories, it could get old quickly.  I would suggest writing out some of the more important stories (the ones that were most pivotal in Hadwin's life) and summarizing some of the others.  For instance...
"As they walked up the hill, Hadwin began to talk again about his childhood.  He related more of the tales about the One he'd learned from his mother.  They were all starting to sound the same to Elanhil..."
Random example.
Also, you might consider giving them an expanded summary.  Instead of writing them out in real-time with dialog, but write out a short (paragraph or two) "plot summary" of Hadwin's tale in the narration.  You can include just one or two pieces of dialog for color.