Getting a job as a J1 scholar by December

My contract as a J1 scholar is running out in mid-November after two years. I have an MS degree from a British university and I am a UK citizen. I have been applying for new jobs as a data analyst so that I can have a new job by the time my contract runs out.

Is my only option now to find another university J1 position? I read that it is too late to get a H1-B.