Jay, true NY style pizza is made with a peel. A screen will adversely effect oven spring and parbaking will ruin the way the cheese melts. If you want to do justice to the style, avoid both.
18" skins are hard to launch. Really hard. They make me nervous, and, for the most part, I feel very confident working with a peel. I would stick to 16" pies until working with a peel is second nature.
Dusting the peel more liberally with flour helps. If you use a ton of flour and spread it nice and evenly, the dough will never stick. Also, sanding the peel with course sandpaper helps creates small pits for the flour to the grab onto.
Peel skills don't sprout up overnight. You just have to keep at it. Practicing with an extra dough ball helps as well. Make the dough ball, top it with a couple pounds of dry beans and then practice launching it on the counter, sliding it back onto the peel, launching it again- repeating 50 or so times. Launch it onto the counter over and over and over again. Put a piece of tape on the counter so you have a spot to aim for.
A couple training sessions such as this and your launching anxiety will be a thing of the past.
Edit: And a 2.5" vertical opening makes launching more difficult as well. I would go down a shelf if you can.