My first turned at 35 weeks, my second felt breech at 36 weeks and I had a lot of pain so was sent to hospital but scan showed she was head down but every time they palpated they were convinced she was breech, even in labour but she wasn't.
The midwives shouldn't really palpate for positioning seriously until 36 weeks and if you're breech at 37 then they will send you for a scan to double check and take it from there. I don't think ECV is offered until 38weeks, and a cesarean isn't considered until 39 weeks iirc from when I asked.
I personally would refuse ECV from what I've heard/read about them. I've had 2 home births and would consider a cesarean my worst nightmare but would elect for one over ECV when it came down to it, and it's a conversation I've had with midwives and my husband in the past (due to the circumstances I mentioned) and they were in agreement.
I would suggest going on the Spinning Babies website for tips. I spent a lot of time in the ironing board position and this time round baby is still very active and lying in transverse quite often and I intend to spend a lot of time swimming when I finish work in a couple of weeks to try and encourage baby into the right position.