You do not reward brand perception with increased payouts, you reward results. Take the names out of the equation and simply reward performance which not only helps the school in every fashion, but also reflects on the strength of the conference. I suggest at the end of a season set aside part of the earnings and divide what is left equally equally among members.
Then award $2 million to conference champ, $1 million for each bowl win, $2 million for each playoff win and $3 million for the NC. That would give a NC game winner $9 million above the average payout, regardless of who that team might be. All teams with successful seasons would be rewarded as well. If a particular team is a net drain on conference revenue for 10 consecutive years, vote them out regardless of the color of their blood.
Clemson or potentially Notre Dame would right now be the most likely to win up to a $9 million bonus. But theoretically it could be NC State or even tiny Wake Forest. And the conference should cover the cost of required ticket purchases to attend a bowl.