Yeah there are some times when I think a single die roll has too much sway over the game: war rolls, first coup or two of the game, quagmire/beartrap. Getting a '1' compared to a '6' for that first coup is a MASSIVE shift for the entire rest of the game.
I'm thinking the game could stand to adopt the Blood Bowl reroll system, which works fantastically for retaining the element of chance while allowing players to tactically mitigate being ruined by a freak roll. Each TS player could get 2 rerolls for the entire game, which could be used on any kind of roll.
And possibly an opening hand redeal system. Both players secretly commit if they want a redeal then reveal their decision to each other. If neither want one, play proceeds. If both want one, redeal happens for both players. If only one wants one, redeal happens for both players but the one who wanted it has to forfeit 2 VP to his opponent.