stretch and sweep advice

Alicia
I have never considered having my membranes swept, however I have had false labor for many nights, and most of the day today. I finally took magnesium and a nap and my contractions stopped completely. I am 39 weeks 1 day. As of last week I was 3cm dilated and 70% effaced. I have been in contact with my midwife who has offered to do a "thorough stretch and sweep" at tomorrow's appointment. I know my baby will come when he or she is ready, and that no kind of induction is natural, but I would like to try the membrane sweep. I don't care if it will hurt, I have been in so much pain for weeks (baby is also at a 0 station and my pelvic floor muscles, hips, lower back, and hip flexors are working overtime!) ...I guess my question is, who thinks that at this point in a pregnancy it is worth it to have this kind of "gentle induction" done? Is it more likely to be successful because I am further along? Is it better to just wait? Even at this late stage, am I risking anything for my baby? Any advice appreciated! I feel desperate.
*UPDATE: had the stretch and sweep done this morning. She was able to get me from a 3 to a 4. She said everything is very soft and stretchy. I am still about 70% effaced. That was about 11:30 this morning. It's now almost 4. The pain wasn't bad during the sweep, just a lot of pressure. Since then I have had more mucus and a tiny bit of pink show, and cramps. BH contractions are normal. The cramping is definitely uncomfortable, but at this point exciting. I hope things move along. I was told to have sex, walk, and try pumping to help bring on contractions. I'll update if anything changes tonight!