pgt: I like your idea of having an option on your turn, though I'd let the option be available for a later roll in addition to the first time.
I know the frustration of having pieces on the bar and the whole of the opponent's home base is covered with a most beautiful prime and you have to roll the dice.
A pass button would be nice. Why roll the dice? Just have a pass button, and then it could skip until the next turn or also have an option for until a point opens for a chance to roll out.
Perhaps a "Pass this Turn" button, and also a "Pass all Turns until a Point Opens, and No Double Offer Made by Me in the Meantime" button?