Well, the solution is simple. The SEC, ACC, and Big 12 are, as of this writing, playing football this fall. So, divvy up the Big Ten teams and play ball.
The ACC has already added Notre Dame, and is playing a 10-1 schedule, with 10 conference games and one out of conference game. Big 12 is going 9-1, since they only have 10 teams. And the SEC is going 10 game conference only.
Ohio State has expressly said they'd play in the SEC. So, fine. Add them, bringing the total to 15. And, the other Big Ten teams that want to play can play with the Big 12.
This would need some changes to be made. First, expand the Big 12 to 10-1. Next, expand the SEC to 10-1. That accomplishes the goal of having the Big Ten teams a place to play and teams to play. It also brings back some rivalries that have been called off.
The SEC-ACC matchups of Georgia-Georgia Tech, Florida-Florida State, Kentucky-Louisville, and South Carolina-Clemson would be back. Ohio State (SEC) could still play Michigan (Big 12). Texas and Texas A&M could return, as could Oklahoma-Nebraska (a Big 12 conference game again). Arkansas could play one of their old Southwest Conference foes. And some other pretty interesting matchups could happen.
After the season, have the three conference champs and one wild card team (gotta give the CFP committee something to do) could pick a team. Heck, this might be a good time to expand the playoffs, since so may bowls will get lost by the other conferences bowing out. Make it eight, or better yet, 16 teams.
If the Big Ten gets all huffy about their teams playing anyway, they can kick them out. Then the new alignment permanent and the Big Ten could go shopping for teams from the MAC to get their membership back up. Or just pick up one team to make up for the five they lost and actually be Ten teams again.
Will this happen? No. Should it? Better than no football.