DD was born as a breech baby after she decided at about 28 weeks that she was quite happy where she was, thankyou, and refused to turn. We declined an ECV and used IMs to ensure they had good breech birth skills. I had the most straightforward and calmest birth of anyone I know, even though it was my 1st and DD was 9lb 12.
Breech birth (hands off, MW led) is usually pretty straightforward - mainly because if the labour isn't progressing well by itself you go for a CS and don't muck around. But a medicalised breech delivery (theatre, stirrups, episiotomy, forceps and a large crowd watching for "education") frightened me silly and I would've had an ECV or a CS in preference to that. This article by Mary Cronk (one of the UK experts on breech birth) sumarises the difference very neatly.
If you want to gather more information, google Mary Cronk and try and get hold of "Breech Birth" by Benna Waites and/or "Breech Birth: What are my options" by Jane Evans. I read them both when trying to decide what to do and found them to be approachable, balanced and informative. There's a chapter in the Benna Waites book on ways to encourage your baby to turn - from memory they include accupuncture / moxibustion, hypnotherapy, the Webster technique (chiropractic) plus a number of variations on the suggestions Poppity's already made.
If your LO does stay breech then it isn't an easy decision trying to decide the best course of action - none of the options are risk free and it really is a case of picking the one you feel happiest with. That said, your MW is right and it IS very common for the baby to move between 31 weeks and birth so try not to worry too much - IIRC something like 20% of babies are breech at 32 weeks but only 3-5% still present that way at birth, and of those more than 50% will be 1st babies and many of the others will have an older breech sibling.
Fingers crossed for you