A few off the top of my head:
1) You've already touched upon it, but I'll mention it anyway because it's usually the first thing you'll want to do. Adjust your pitching staff. If you ran a 5 man rotation, you can probably go with a 4 man (or a 3+ man) rotation in the postseason because of all the off days. You can either put the removed SP's in the bullpen as long relievers, or replace them on the roster with setup guys. You can even drop a pitcher and add either another bat or defensive SS. Also, no need for a mop-up guy. Your staff should be ready to pitch to win for nine innings every game.
2) If you use auto-rest setting in the regular season, turn them off for the post-season. There's no room for resting guys in a playoff game. They should play all nine innings, unless removed for a pinch-hitter, pinch-runner, or defensive replacement.
3) Make your call bullpen settings more aggressive. You can't afford a pitcher blowing up into a big inning for your opponent in a playoff game.
4) In an elimination game, everybody is available to play. Don't hold a pitcher back for tomorrow if there's a possibility that there is no tomorrow. Everybody needs to be available to help you win today.