Yes baby definitely still has time to move! With my DS1 he was breech up until 39 weeks and moved just before my planned section! Currently 37 weeks with DC2 and breech again, but hopeful that they will move too!
Have a look on spinning babies and YouTube, there's loads of good videos to encourage turning naturally
Hi OP just an update for you - I'm 38 weeks now and at a scan today baby is head down! At 36 baby was breech. Didn't feel a big movement, my babies just clearly like being breech up until the last minute!