I'll get the ball rolling with the easy points. These ones have only ever been played live once.

These Arms Are Open All Night from Borgata Events Center, Atlantic City NJ, November 21, 2004
Available on an unofficial DVD release, it's also on YouTube.

Only In My Dreams from same as above.

Love Ain't Nothing But A Four Letter Word from same as above.

Open All Night #2 from same as above.

Why Aren't You Dead from same as above.

Thief of Hearts from Borgata 2003. TLFR DVD I believe.

Sylvia's Mother (Dr. Hook cover) from same as above.