Walking, also walking up and down stairs, although it's not as easy or fun as it sounds lol good luck!!
37 weeks they are pretty much done. I am pretty much done with being pregnant by then as well. It sounds like your body is starting to go naturally but I really think walking helped with my babies. Lots and lots of walking.
The baby will come when the time is right, why do you want to rush things? The longer they stay inside the better for them, up to 41 weeks is completely normal.