Possible gap in employment under J1 visa, with offer letter at hand

[Saamik]

I am an employee at West Virginia University working as an engineering scientist under the J-1 visa. Recently I have received an offer from Texas A&M university for working there, and I am nearing their onboarding on March 1st. In this regard, I have also resigned from my current employer. And they have started the process of off-boarding me.

Last Friday, I became aware that the Texas A&M has not started the J-1 visa transfer process because of some miscommunication, and they indicated that it would take almost two month before the visa transfer could be processed.

At WVU, I still have some annual leave which I could encash, but, I can also utilise it towards being on the payroll for additional days. My current employer is willing to reinstate me, but he mentioned that it has to come through an offer letter, which given it has to be signed by the provost, may take considerably large amount of time.

What are the options in my hand, understanding limitation of both the universities, so that I don’t go out of status.