I booked an induction massage for 3 days after my due date. It works on pressure points so I thought could be a nice way to give baby the message. I was then going to step it up to acupuncture... I'm like you and didn't want to make aby come early if they're not ready but I decided a few hints might not hurt to take away the pressure of a medical induction.
In the end my baby came 3 days before the due date so I can't give feedback on these methods sorry. Oh, I drank RLT and took the tablets throughout almost the whole 3rd trimester and my uterus worked like a dream.