Simon,
I think the idea of simply making a stadium pick in conjunction with a player pick at any time you want to during the player draft is the way to go. That way, the guys who want to wait until Round 6 to pick their stadium can do so, and the guys who really want a certain stadium can pick it in the 1st Round, or during any round in between.
If you decide to stay with the separate stadium round, do you want me to make that first pick any time today, or do you want me to wait until 7:30 to kick off that process?