I won't be agreeing to sweeps or induction either.
Mine keeps moving up & down. Was 3/5ths engaged at 36 weeks but on Monday morning was "free" (not engaged at all). I can tell as well because at 36 weeks I felt hiccups really low between my cervix & bum lol. On Monday lunch the hiccups were felt near my belly button. But by Monday night late on I was feeling them really low again.
Also sometimes when s/he moves it feels like the baby is hitting/rubbing against my cervix and sometimes feels like it's bumping or squishing my bladder. So I really think it bobs up and down regularly lol!
I don't think there is much you can do to go into labour naturally.
Fresh pineapple, hot/spicy food, sex, long walks/exercise, are all supposed to start labour but I think it only works if you're ready and about to go into labour anyway.
I ate a whole fresh pineapple on Monday night haha. It was lovely but it didn't work.
Also had a hot curry (Madras) from a takeaway last Friday night.
I've halted all attempts to labour now, I'm holding out til next Thursday night as I want the baby to be born on Friday the 1st now lol.
I've ordered a fresh pineapple (again!) with my food shopping that's coming Monday. And think I might have a spicy curry from the good curry restaurant on Thursday night, pineapple for afters LOL!