If you're really connecting with someone the content isn't that important. You want to let an atmosphere, a feeling happen, that's why focusing almost solely on content doesn't work that great. In fact, it can completely get in the way because you're thinking about what to say next instead of paying attention to to what really matters: Being in the moment with her and allowing the conversation to go somewhere productive and fun.
If the speaking part of your performance is off, you'll know if because you will suck at charming women on the phone. If your phone convos go great but you suck ass at meeting women in bars, then it's not the content that needs fixing, it's your image, the aura you're projecting, and the fact that you're not using vibe creating and smart body language/paralanguage. Even the position I am standing or sitting in will be more important than remembering that great story from the Internet.
Anxiety does reduce cognitive resources. People speak at about 150 words per minute or less. Your brain can process about 500 words per minute. You have lots of resources even if she were talking nonstop, but as the OP mentioned anxiety can cut this difference down. Specifically in bars men can be affected by stereotype threat. This occurs when they think people in clubs can tell "this person isn't a club guy, or he doesn't belong here I bet he sucks at socializing in here" and because they are afraid of confirming the stereotype of "being a person like that", the performance actually goes way down. That's why some people use positive visualization to help deal with this. Additionally, learning any performance art that requires being on stage should help with anxiety. If you can play music or give a large presentation, talking to a girl might seem pretty safe in comparison.
