Some other options, just for fun:
A Golden Batter out is worth two outs. In the next inning, the other team is permitted four outs instead of three.
If you use your golden batter, you start with 1 strike.
Golden Batter must be immediately substituted out after that plate appearance.
Use of your Golden Batter is a replacement for your first Manfred Man. So if you use your Golden Batter to tie the game in the 9th, you lose your Manfred Man for the 10th inning.
Use of your Golden Batter is only allowed if you have not previously used your replay challenge.
Use of the Golden Batter requires that the Golden Batter's team's broadcast must be replaced by John Schriffen for the remainder of that half-inning, and the two additional half-innings.
The Golden Batter must be selected by a committee of recent Sox Math winners. Also, all teams must have an equivalent contest to Sox Math.
Use of the Golden Batter negates any fielder positioning requirements, so extreme shifting is once again permitted for that plate appearance.
The next time the Golden Batter's turn in the order comes up, the opposing team may choose the batter for them.