my 1 year old had this same problem starting at 8 months. Its not the diapers issue. Its just that they are playing and sitting in it for a period of time that the activity works the poop out the top part of the diaper or leg. Especially if its a wetter poop. Unless your right there to clean them the minute they do it and they are not sitting in it for more than 5 there isnt much you can do. In my sons case, he likes to sleep on his tummy and elbows, with his butt sticking up in the air. I have resorted to buying a bunch of cheap crib sheets, putting a catch sheet under it to keep the mattress clean. I dont put any clothes on him save a diaper, I keep many extra blankets around, I give him 2 blankets. Though he is needing a bath everyday it saves my sanity of having to get the disgusting clothes off him. He still does it occasionally at night and he is 1 now. So I am hoping it ends soon. He is in size 3 as well and I tried 4 and 5's it doesnt help.
EDIT AND ADDITION: I love Luvs. I have tried Pampers, Huggies, they suck for my son. Not for every child though, but for my son they do not work worth, well- a poo. Luvs can take like 3 pees and a poop before a change in a pinch LOL. Cheaper too and thinner. They are not bulky like Huggies and Pampers. Though they are not soft the are more papery. My oldest couldnt handle Luvs on her skin she was a Pamper girl.