Thank you for some fabulous advice! I really should have thought about the walking foot before, so I'll definitely try that next time (I have a bunch of other placemat tops ready to be made up!). As these ones are already done, I might just put some binding on them so that the pucker is covered up, as I want to try and sell them, and these are not up to scratch for that at the moment!
I think the order I did was batting, backing, top (from the bottom) and I did pin the sandwich, but not with very many pins, so maybe I need to pin it more thoroughly next time!
I like the sound of the 45 degree sewing off the edge to help with turning under! I definitely found that part the hardest, so I think that will really help!