I have to amend my scenario. The first BC-ND game was not until the 1970s and the Eagles did not play Pitt or Syracuse consistently until the the 70s as well. I see little impetus for them to be included in this hypothetical conference.

Maryland is also a huge question mark. They were disgruntled in 1953 but I don't know that there was mutual attraction between the Terps and powers at be in this league.

My revised scenario looks more like this:

In the 1950s Michigan decides to join the more successful league that has ND, Mich St, Ohio St, Cincy, Pitt, Penn St, and Syracuse in it. This paves the way for schools like Purdue and Northwestern to make similar moves leading to a 10 team conference. ND likely demands that the number of conference games be low to accomodate rivalries with Army and Navy. (The annual USC-ND series that began in 1926 never materializes because conference membership allows the Irish to schedule closer to home)

The result is that a weakened Western Conference and Big 7 combine to form the Big 12:

South: Colorado, Oklahoma, Kansas, K St, Nebraska, Mizzou,
North: Iowa St, Iowa, Minnesota, Wisconsin, Illinois, Indiana


This 1950s merger probably means no partial Big 8/SWC merger which might mean some Texas schools accompany Arkansas to the SEC in the early 90s.
It's hard to say what happens with BC football. They either decline and join Rutgers and Temple as weak eastern independents since they struggle to schedule significant competition or maybe they hang on and join a major conference in the 1990s or 2000s.