My baby was transverse/breech/very mobile between 30 and 36 weeks resulting in an ECV at 37 weeks (I'd tried elephant walking, bouncing on the ball, handstands in the water, front crawl, knee chest position, acupuncture, moxibustion, inversion and possibly some other things) - I read this before I went in and it really really helped relax me (partly because this is the consultant who was doing my ECV) www.motherhood.org.uk/2normal220404.htm
She reassured me that she found, generally, drugs to be less helpful (this is my second baby, which helped) and she said that my ability to relax was very good and very helpful. She told me to tell her to stop at any point, it was relatively uncomfortable but I found deep breathing helped.
They monitored me on CTG for half an hour afterwards to check baby was OK. Was told that they also perform ECVs on women at 37-41(+) weeks, and sometimes many times to get success.
Have been sleeping on RHS for over 4 weeks as she said that baby had stretched my uterus and was worried baby would 'flop' back to transverse. Still cephalic now, 4.5 weeks later (overdue and free, but cephalic!).
I also researched breech and found that my local hospital is supportive of vaginal breech births.
Good luck