Help needed in J-1 transfer, thanks!

Hi there,
I am currently holding J-1 visa as a visiting professor at a university. I got a permanent job offer as an assistant professor which will start from August 1st at another Univ.. The problem is: my J1 will be expired on June 30th and there will be a time gap( July 1st-July 31st) since I didn't sign next school year's contract with the university that I am currently working for. Could you please tell me how I can solve this problem? Is it complicated for J1 transfer? I have heard O-1 Visa, is it possible for me to apply one?
Thanks for your help!

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