What I can't believe is that you have no pre-1966 music on the list. The earliest song you have on there is "Tomorrow Never Knows" off Revolver. There are a ton of songs I would add. I would subtract "Dont't Let Me Down," "I Me Mine," and "I Want You." I actually like "Rain." Problem is, I really want to add more than three. I've listed a bunch, but given the addition/subtraction rules you have laid down, the first three are the ones I guess should really be on there.
1. "Run for Your Life" - Rubber Soul
2. "No Reply" - Beatles for Sale
3. "You're Gonna Lose That Girl" - Help!
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"Thank You Girl"
"Please Please Me"
"Love Me Do"
"Think For Yourself"
"In My Life"
"All My Loving"
"It Won't Be Long"
"Eight Days a Week"
"I'm A Loser"
"You've Got To Hide Your Love Away"
"Things We Said Today"
"And I Love Her"
"Fixing A Hole"
"Getting Better"
"Something"
"Fool On The Hill"
There are a bunch of other ones. I would encourage you to start at the beginning.
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It's been emotional.