I'd recommend you get rid of the tire and use a brand different than Vittoria. I've had the same problem as you - the sidewall bursting from what should be a simple pinchflat. Continentals are good. Also good are Michelins, which are what I ride on my commuter.
You are right, the dollar bill trick only gets you home, especially if the tear is more than a couple of millimeters in length. As for recycling, perhaps ask the bike shop? I don't know. I have to admit that I just throw it away or tuck it back into the corner of the garage if there is life still left in it for use as a spare - not an option for you with a sidewall split.
__________________
Cat 2 Track, Cat 3 Road.
"If you’re new enough [to racing] that you would ask such question, then i would hazard a guess that if you just made up a workout that sounded hard to do, and did it, you’d probably get faster." --
the tiniest sprinter