The just do it mentality definitely won't work of course! And this cannot be cured because it's not a disease. It's almost like an involuntary motor function. You just have to unlearn the stutter, and learn fluid pronunciation. If that's the case you can come up with different ways to learn. Why I recommend singing is because you hear how you're supposed to sound from the artist. You know what you're supposed to say from the lyrics. You're taking the work out of your brain to come up with things to say and how to say it, and replace it with what to say and how to say it.