It can be simpler than that. Just randomize which team starts each round, and everyone else follows. That way you always follow and precede the same people, so it's quick to sitemail.
#1 starts the first round, followed by 2-3-4 ...
#8 might start round 2, followed by 9-10-11 ...
#20 might start round 3, followed by 21-22-23
Everyone gets a turn in every spot, but the team that picks 24th in round 1 might pick 8th in round 2, 13th in round 3, 3rd in round 4, etc.
But if people want their draft times to just shift forward by a half-hour every day, randomization doesn't work.