You should get smoother Italian ice and not the kind you would find in a regular grocery store, if you have the chance, because that would probably solve a lot of your problems. Or not...maybe just the fact that it's naturally cold is the main problem. If that's the case, I'm not sure a different eating method would even work for you. I eat it the way most people would expect, using mostly my tongue for smaller quantities, and a spoon for larger quantities.
My favorite place to get Italian ice from is at the Lemon Ice King of Corona on 108th Street and 52nd Avenue in Corona, Queens. Very wide diversity of flavors, authentic and much better than Ralph's and Uncle Louie G...simply the best Italian ice place anywhere, though most people here probably don't live anywhere near it. I was most recently there yesterday and I've been going there for years.