I tried this the other day and it worked to perfection, so I thought I should share it.
In a Showdown wherein you must score a certain number of runs before making a certain number of outs, there is one setting which is hugely advantageous to the player...
UNDER NO CIRCUMSTANCES WILL THE CPU CHANGE PITCHERS.
I was in a 12-out Showdown against a closer (can't remember which), and as it started the thought occurred to me that he'd have to pitch well enough to keep me from getting hot for four-plus innings. I proceeded to make every at-bat take as many pitches as possible to tire the closer out. I never swung with fewer than two strikes in an at-bat and hit many deliberate foul balls.
By the time my leadoff hitter came around again, the CPU closer threw 13 consecutive balls. Before it was over, he'd put six hitters in a row on base, walking four and hitting two. I ended the Showdown on a simple bunt, with the computer happy to give up the winning run in order to get a 3-6-1 double play.
That's the other thing to remember, by the way: the CPU is playing normally, as opposed to trying to win the Showdown.