If I didn't have a 16-inch screen and didn't want to use one but I had a 16-inch stone or a large tiled area that could accommodate a 16-inch pizza, I personally would just go out and buy a larger wooden peel--one with at least a 16-inch blade and possibly closer to 18-inches.
Another way, which I once tested on a metal peel with reasonable results, was to put a sheet of parchment paper (it has to be the wide parchment paper for a 16-inch pizza in your case) on the metal peel, and put the shaped pizza round on top of the sheet of parchment paper, dress it and then slide it onto the stone. As a precaution, you can put a bit of flour or cornmeal under the parchment paper between it and the peel to insure that the pizza will slide off of the peel and onto the stone. To prevent the edges of the parchment paper from scorching, I would cut the sheet of parchment paper to conform to the size and shape of the pizza with about an inch or two to spare. You can bake the pizza for the entire time on the parchment paper, but I found it better to remove it once the pizza sets up, which is usually only a couple of minutes. You just lift the pizza (I use my fingers but any tool will do) and remove the parchment paper by grasping it at the edges. From that time forward, the pizza bakes in the normal fashion. If you wait too long to remove the parchment paper, it can become brittle as it is exposed to the high heat and be almost impossible to completely remove. I find this exercise a bit of a pain, and over time you will go through a fair amount of parchment paper (which is not all that cheap), which is why I would just go out and buy another, larger wooden peel.
As for managing the dough during shaping, my practice is to work and shape the dough on a large wood cutting block that has been lightly dusted with flour. I also dust the dough ball, which I first flatten (if it already wasn't done before) very lightly on the top and bottom with flour. I try to use the smallest amount of flour necessary to insure (I hope) that the shaped dough won't stick to the screen (or a larger wooden peel if I had one). When I am ready to transfer the shaped dough to the screen, especially one as large as 16 inches, I fold the dough round in half, and sometimes even in quarters--just as is often done when transferring a pie crust onto a baking pie dish--and transfer the dough to the screen and unfold it. If the dough needs any final minor adjustments to size or shape, this is when I do it. It is then dressed. I reduce the likelihood of the dough sticking to the screen during dressing by having everything I intend to put on the pizza all laid out in advance at my work area.
In your case, where you are building the pizza on a metal peel, and especially because it is metal, it is a good idea as you are building the pizza to shake the peel a few times to be sure that the dough slides. If it doesn't or it is sticking in spots, you may still be able to lift the dough from the edges and toss a bit more flour under it. This is a lot harder to do when the pizza is fully loaded and dressed. So it is very important to have all of the ingredients you intend to put on your pizza all laid out in advance and to work fast. I have read that it may be possible to dislodge a stuck pizza from a peel by using a length of dental floss and running it under the pizza from edge to edge, but I have never tried that to confirm that it will work.
I am sure that there are others more inventive than I who have their own handy tips that they fall back on when they are making their pizzas and have to deal with the issues mentioned above. Maybe some will come forward with their favorite tricks.