Boss Did Not Accept My Final Date And Calls My Future Boss

I work in a college, and got a better position in a different college under the same institution. Two months ago, I told my Dean that I was among the finalists for the position in the different college. Once I received the verbal offer, I negociated the starting date for 3 and 1/2 months later, but HR was very slow and I only received the contract 5 weeks from the starting date.

Once I signed the contract, I immediately informed my Dean, who said he could not accept the final date, stating that my contract requires 3 months notice. Employment in California is at will and the employee handbook stated that "it is customary to give 3 months notice". When asked about the reason, he said he was concerned about who would take care of some of my responsibilities.

Within the next 2 days, I consulted with HR about this requirement and talked to my colleagues and supervisors who identified potential replacement to my scheduled activities. All colleagues were super supportive! HR confirmed by email that I can start the new position as per the contract. I forwarded the info to my current Dean and explained that his concerns have been addressed, but he refuses to accept the end date. He replied that he was talking to HR, the Provost, and my future Dean! They all know each other very well! I am afraid he will create a bad impression to future boss and I end up starting the new job under suspicious and scrutiny.

My new contract was signed by the new Dean and the Provost, and approved by HR. No one mentioned any 3 month requirement. I remain collegial, professional, and very respectful in all my communications with current Dean. I did send a mass email to my colleague thanking everyone and informing my departure, with the end date on it. I don't want to stay longer here because the leadership is toxic (colleagues are great, thought).

What should be my next step?