There might be better alternatives to serpentine for the four rounds. Teams could be placed into blocks of five to spread things out more evenly, with each group of five picking 1-5 in one round, then 6-10, 11-15 and 16-20. So a team might pick 3rd, 8th, 13th and 18th intend of 3rd, 18th, 3rd and 18th. That would give each team an early, early-mid, late-mid and late pick. A reverse option would completely much up the fairness of that plan, though.