I use a 16-inch screen because my peel (wood) is not big enough to hold a 16-inch pizza and my pizza stone is similar to yours in that the major dimension is 16 inches. What I do is bake the pizza on the screen until the rim of the dough starts to turn brown and the cheeses bubble, and then transfer the pizza to the stone for a final few minutes of baking. At that point, the pizza is stiff and overlaps the stone, but the overlapping is of no consequence. While I haven't done it, you could bake the pizza only to the point where it just starts to stiffen and then transfer it to the stone, where the bulk of the baking will take place.
Some people use only the 16-inch screen for the entire bake, and don't use the stone at all.
As Canadave has pointed out, another possibilities include getting a larger peel with a larger blade and replacing your stone with tiles with a total surface area large enough to hold a 16-inch pizza. You could also get a larger pizza stone, and I have seen some advertised on eBay at reasonable cost (I think the stones were 16" x 16"), but the larger stones I have otherwise seen advertised from conventional suppliers tend to be quite expensive.