The repeated scenes to me kind of relate on how Fei keeps thinking about these clips/memories in order to try and remember her past. So I kind of think that they are essential... but that's just my opinion.
Another thing that I like is the ending. The ending in the current verion with the "See you Cowgirl, someday, somewhere!" I like. Also in the end of the current version when Fei makes her comment about trying to see her self 10 years in the future and hearing her turning off the tv I find very funny. ^_^
It also seems like your timing on the current verion is a little better. I cant tell if that miss timing was intental or not.
What I like about the first verion is there are a few scenes that fit a little better. Such as the clip played at "I don't want to hear who walked On water, because the hallways are empty" with the broken lion fountain.
"Women are scary."