Not to be nitpicky, but rather to help: You are using 'me' and 'I' backwards. It's really distracting and made it difficult to get through the beginning of the post to the actual story.

The rules are simple: Take Carl out of the sentence. Would you say "Me made myself available"? No. Then why "Carl and me made ourselves available"?

Would you say "score extra points with I"? No. Then why "score extra points with Carl and I"?

If you are in the subject of the sentence, then use I: "Carl and I went to the movies."

If you are in the predicate, or are the object of an action, use me: "The students handed their completed tests to Carl and me."