Hey! Native English speaker here. When I started learning German I became aware that I didn't stutter, or if anything it was a lot, LOT less. I think this boiled down to the fact that my mind wasn't concentrating on me stuttering and feeling silly etc, it was just on what the word should be and how to pronounce it. Maybe you are working yourself up about the pronunciation and getting excited about showing it off, that you get scared it wont look good and so you worry about the stutter more than getting the correct word? That's what I would guess based on my own experience, but for you it could be entirely different. Hope it helps!