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One of the BGDL podcasts dealt directly with this, and one of the methods was the player count +1 method, like you’re suggesting, so there’s more dice to pick from, but the one that sounded best to me was the “snake” method where turn order would go 1-2-3-4-4-3-2-1. Maybe a hybrid version of moving start player and that would benefit? You could have 2 dice for each player then so each “round” would cycle through that snake once before passing along the starting token.
