To speed up the game when playing AI adversaries (should one wish to) i would consider adding a "Skip spectating" per Spectator screen. I know this can only work on AI "players" and realize that you would miss out on knowledge you gain when looking at what they do BUT i also think the speed up and sense of realism in that you would tend to make bad calls as you dont have the information, would make the game more like a gang fight meaning fast paced and harder to win.

I do really like they way you have taken a tapletop game to the PC and made it feel like a tabletop game still, but normally the waiting period is part of the game complete with (possibly) witty banter and reactions in the form of defensive dice-throwing.

I believe the above would make the game even more enjoyable with out having to tackle too many serious issues because the default would be spectating and it would be a choise, so those critical ones some really would like to see, they still can.