So if we set the sign-up deadline at 2 PM EST of January 14 (remember I'm operating +6 from EST, so that's 8 PM for me), then the tiers/segments could be announced right away and the lottery for the top segment (picks 1-4 overall) would be held. Neither would take long.
Next step: the reward lottery for the remaining GMs who are eligible for a reward. Would be done right afterwards and wouldn't take long either. First a random order will be determined for rookie GMs plus the GMs who voted 6/6 times last year, then for the GMs who voted 5/6, then for the GMs who voted 4/6. Each GM has time until the next day (let's say the deadline is 2 PM EST on January 15) to announce an individual ranking of the segments in order of their preference. Of course, GMs can also choose not to announce if their draft position doesn't matter to them.
Once the deadline has arrived, I will assign the GMs to their preferred tiers/segments in sequence of the reward lottery order. That being done, the main lottery for all the picks (save 1-4 overall) follows. In case a segment is already fully assigned, all I have to do is hold a quick lottery between the four or five GMs to determine the order. For example: GMs A, B, C and D have been assigned to segment II (picks 5-8 overall), so all that is left to do is to let the dice decide who among them picks 5th, 6th, 7th and 8th. The unassigned GMs enter the lottery as soon as a segment that has not been fully assigned comes up.
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At this point the above is only a suggestion. Thoughts?