I doubt that you would be able to re-enter. I had a similar situation a few years ago when I was still H1, before I got my green card. With H1, you can get extensions after the original H1 visa has expired that allow you to stay in the US. However, when I wanted to do a business trip, I had to apply for a new visa at a US embassy outside the USA before I could return.

Your situation is a little different, but the similarity is that you have an expired visa, but are still allowed to be in the USA.