I would certainly be interested in participating regardless of the formal set up.
Timeline: 6 months seems like an unnecessarily long amount of time. A month should be sufficient, but I might have more free time than others.
Partner Selection: Letting people choose partners would probably be the simplest thing. If someone had two people who wanted to work with them, would they be able to make separate submissions? If pairings are not made by choice, you'd probably need a sign-up period prior to the contest to ensure you'd have an even number. You could use a RNG initially, and perhaps use a round robin system later on (with the winning team gets first choice of partners.)
Responsibility: The way you've phrased it, you've made it sound as though the co-writer is a junior partner or editor. What is the difference between the writer and the co-writer?