I have heard that trying to express (gently) or stimulating the nipples can help to bring on labour. Cant hurt to try.
I mean the list of things to bring on labour is long, castor oil, spicy food, sex, exercise...............
But this is the only one I have heard of that seems to make sense in regards to the link to the uterus.

I was 11 days overdue with DS so I truly feel for you. GOOD LUCK. Big hugs and LV's going your way. Have you had a stretch and sweep?