If you think the transfer portal is causing chaos in college athletics, the players have nothing on the grownups. Football coaches across the country are jumping to new, richer jobs, with some leaving their teams at the most critical time of the season.

Conference championships are at stake this weekend, with winners advancing to the College Football Playoffs. Ole Miss will be there after a historically successful season, but without its head coach, Lane Kiffin, who was shown the door after accepting the head coaching job at LSU.

Mr. Kiffin wanted to remain the Rebels’ coach through the playoffs, but the school administration wanted him gone immediately, elevating an assistant coach to lead the team in its first playoff appearance.

By contrast, the American Conference championship game on Friday features two coaches who have agreed to new jobs for next year but are being allowed to finish out this season with their current teams.

North Texas’ coach, Eric Morris (headed to Oklahoma State), and Tulane’s Jon Sumrall (bound for Florida), are being allowed to complete their season as a sign of gratitude. The winner between Mr. Morris’ No. 20-ranked Mean Green (11-1) and Mr. Sumrall’s No. 21 Green Wave (10-2) is expected to become the Group 5 representative in the 12-team tournament for the national championship.

“Not a ton of people really know what we’re going through and how hard some of this stuff is and how hard the decisions are,” Mr. Morris said. “Ultimately, I think it’s really cool that we’re kind of in the same position right now, and that we’re both still able to lead these teams that have fought so hard for us.”

Mr. Sumrall expressed gratitude at being allowed to continue to coach his team. “When you have a chance to pursue a championship, there’s nothing like it.”

The job moves are far from isolated incidents in a profession with plenty of high-profile openings. LSU fired Brian Kelly in October, joining Penn State, Arkansas, UCLA, Stanford, Virginia Tech, Kentucky, Oklahoma State, Auburn and Florida in making changes at Power 4 schools.

Mr. Kiffin’s name was linked to LSU and Florida, creating weeks of speculation and distraction as the Rebels completed an 11-1 regular season. Pressed by LSU to make a decision, he accepted a seven-year $91 million offer this week, infuriating Ole Miss fans and administrators.

The legendary coach at Alabama, Nick Saban, doesn’t like any of it. “None of this is fair to the players,” he said on ESPN’s “College GameDay.”

“This is not a Lane Kiffin conundrum. This is a college football conundrum that we need some leadership to step up and change the rules on how this gets done in terms of coaching searches and opportunity for people to leave.”

Mr. Saban suggested the college ranks adopt the NFL model where a coach can be contacted only after the end of his team’s regular season and at select times during the playoffs.

“We need to take a better approach to the business aspect of what we do in college athletics,” he said. “In the NFL, you cannot leave your team until you’re finished playing. You can’t talk to another coach in the regular season. There’s a defined time where you can talk to them if they’re in the playoffs. That’s the way it should be.”

Most coaches don’t seem to mind the current hiring process. Even getting fired pays millions. Mr. Kelly will collect the remaining $54 million he’s owed from LSU after suing the school to enforce the buyout.

Mark Stoops is owed roughly $37 million after being fired at Kentucky. Under his contract, Mr. Stoops was to be paid the entire amount within 60 days but has allowed the payment to be spaced out over several year

James Franklin was due $49 million after being fired at Penn State, a figure that will be reduced dramatically after he accepted a job at Virginia Tech. Michigan State will pay Jonathan Smith $33 million and Florida owes Billy Napier $21 million after cutting ties. Auburn’s former head coach, Hugh Freeze, must make do with $15 million.

With millions in buyouts, backroom negotiations, in-season departures and accusations flying in every direction, the adults shaping the sport have created a landscape more unruly than anything happening in the transfer portal.