What I do now is shape the dough on parchment paper, put the paper and all on the peel, and launch it onto the stone from that. After a few minutes on the stone, I reach back in there and give the paper a quick tug, like when a magician pulls the tablecloth off a fully-set table and leaves all the dishes in place.
The only bit to be careful about...that parchment paper is slick, and I've been in a hurry and let one fly right off the peel and onto the kitchen floor while on the way to the oven, and just the other day, I was in a hurry and launched it a little too aggressively, and it overshot the stone and slammed into the back of the oven and down onto the oven floor.