There are so many things you can do with absolutely huge shrimp. The largest shrimp we get at work are 8/12 count. Basically, those shrimp weigh anywhere from 1 1/2 - 2 ounces EACH! They're about the size of my fingers, maybe bigger. You can stuff these things if you're carefull.
I, too, do not relish the thought of peeling a lot of small shrimp. Luckily, I can buy a 2# bag of 40/50 count peeled and deveined shrimp at work for about $13. That's quite a bit of shrimp!
Look around for the best deals on shrimp. You might want to look in the freezer section of a local grocery store, and see if they have any 5# boxes of frozen shrimp, which is how most shrimp is sold, even to restaurants. Be sure to read the label, to get size (16/20 is a good size for home use), whether they're peeled, deveined, head-on, head-off, etc. I actually found a good source of these, of all places, at a Chinese grocery store. They were actually selling restaurant products retail to the public.