How exciting! Due dates are funny things. Almost all of our pregnancies went over (except the twins, which were almost exactly 40 weeks and that is late for twins). Our first was almost three weeks over. Due dates are really only estimations. Doctors can start to get concerned after 41-42 weeks, but we had home births and our midwives never felt like medical inducement was necessary.
My wife tried all kinds of things to help move it along, maybe they helped, maybe not. We'd go on walks, she'd sit on an exercise ball, we'd even have sex because she heard that semen softens the cervix. Haha. I think she took some castor oil for one of the pregnancies. DYOR there. It has a laxative effect and is believed to help induce labor as well. There are some chiropractic maneuvers that can help break her water, but you don't really want that until labor has actually started but is moving very slowly, as it did for my wife.
Cheers again to you two. It is an exciting time, but also very strange, like you said, to be stuck in this in between place.