How about if you tell them that for that leg of the trip you'll be traveling with a huge musical instrument or painting which is too fragile to be placed in baggage. Would that work? I've heard of musicians being required to purchase a seat for their instrument.

Also, what if you tell them that your cousin has the same exact name and will be traveling with you on that flight. More generally, how do they deal with all the people who share common names?

Anecdote: many years ago a friend of mine traveled together with not one, but two cousins who all share the same exact name. I don't know how they managed the booking w/o trouble, but during check-in the agent got so frustrated with the third one sharing the same name that she initially refused to check him in (what i understand is that she had cheked-in the wrong passenger for one of the first two and when the third one showed up it said that he was already checked-in)!!! it was resolved in the end before the plane took off, but they said that the agent was freaking out on them.