The far superior Crunchwrap Supreme was practically engineered to solve every case of taco mishap imaginable. Crunchy, tasty, and sh*t doesn't fly everywhere when you bite into it. It even keeps your hands relatively clean. If you must eat in your car, this is the way to go.
The only flaw is it doesn't have a good way to inject hot/medium/mild sauce into the envelope, and I'm pretty sure you can't order it prepared that way.
You can. I worked at Taco Bell, and our managerial training had/has an entire module that boils down to: "if we can reasonably do it, and the customer asks, then do it."
That's the one with the soft taco shell bean-glued to the outside? Solid compromise to prevent taco-shell shrapnel from ejecting all over your lap. Doesn't fix OP's cheese problem though.