Thanks for the replies. Some useful advice there. I had used parchment myself in the past, when I had a conventional oven, but I worried it would catch fire in my new, hotter oven, which reaches 650 F. I'll try it.
I take your point, Mark, about the feel of the dough. But part of the reason I have problems is because I like to get the pizza ready maybe half an hour in advance of putting it in the oven. I know that if I stretch out the pizza, add the toppings and put it in the oven straight away, it generally won't stick. But I'm usually cooking multiple pizzas for a group of people and I like to get them all lined up. Otherwise I won't see my guests until after they've finished their food, because I'll be stuck in the kitchen! When you have a pizza sitting around for half an hour it gets sticky again, especially if you're using a wet dough like Jeff Varasano's.
I know it's frowned upon to leave pizza sitting around for half an hour before putting it in the oven, but I find it makes little difference to the cooked dough. It's just that it's more difficult to get it off the peel.