YES

Yes, you can. Your situation is similar as my family. I got green card about one and half years ago, but my hu*****and's was stuck to the name check for more than one and a half years. I quit my job after I got my green card because of my health issue. I was so worrying about if this will affect my hu*****and's case. Finally, my hu*****and got his case approved yesterday. So I think you will be fine to quit your job.