It's cool you are a capable public speaker. Based on what you wrote in this post, my first thought is about time and you perceiving urgency. When speaking publicly, one-on-one, or formally, there is much less time-based pressure. It feels like it's your time and you can speak at whatever pace you want to. More casual conversation in groups or question/answer moments feel more hurried because you will see a lot of individuals appearing to speak effortlessly and offering immediate responses. Maybe you should try to intentionally bring in your sense of control of the pace of the conversation by putting in a pause or two. Silence always feels awkward but it's completely fine to give yourself some time when you want to. I'm not saying intentionally grind the conversation to a halt, but get used to showing yourself it's ok to speak on your own time. I'm not a professional or anything, it just seems like it may help you a bit based on what you said. Someone else mentioned giving yourself permission to stutter, which I think is probably the most practical and useful thing we can all do.