One piece of advice which I think should be applied to every tournament:
I would like the drafts to be made 24 hours before the games are played.
For the spectators it doesn't change a lot, specially in recorded games, but if the drafts are published, we can gather all together starting to debate who will play every civilization and in what map, increasing the hype (Similar to when the sports press debates all week about what players and what combination will Zidane use in the Clasico). It will also provide more content for casters (la previa, Memb)
For live games, less loss-time before and in between games, as the players will already have most of the discussion made.
For the players, they may have 24 hours less to prepare the draft, but they gain 24 hours to actually think about the civilization and prepare actual strategies instead of maybe loosing all the preparation because they didn't get a critical civ in the draft. . I tournament I played followed this rule and I saw it as a great advantage
You still only have 30 seconds to pick a civ so they would think of strats with what they have left in the draft.