Some thoughts from a Badger fan who lived in the Cities for a few years:
The Gophers have yet to develop a large enough "rabid core" to both sell out TCF and convince Bowl sponsors that they are desirable. I agree with another poster that a Rose Bowl breakout season would help, but you need a fairly large consistent core who travel, no matter what. Example: In my family, the family Christmas celebration has been moved because so many of us go to the Badger bowl game - wherever it is - every year. While some might think that is odd, with half the family going, the Bowl Game itself is a family event. Minnesotans haven't developed that culture.
As many here have noted over the years, Gopher football is not yet an "event" separate from the game. I think you have the ability to change this one more quickly than developing a larger "rabid core," but the Athletic Department must make it fun for the average fan and the corporate types. You need to make getting a Gopher ticket a hard-to -get commodity and making it part of a total Game Day experience should be a priority.
A program to give away unused corporate tickets to Boys & Girls Clubs or local youth sports teams would help put butts in the seats would help with the empty seats. [Not sure why UW doesn't have this issue, but those seats may all be inside.]
Winning will help, winning big will help a lot, but you really want a large contingent that will travel for the event, not the game itself. That is harder to build, but a Rose Bowl or similar game (realistically, what is similar?) would do wonders.