Everyone around me speaks so fast, it makes my speech worse.

Everyone around me speaks so fast, it makes my speech worse. I want to be comfortable speaking at work and showing presence. However, one of my anxiety/block triggers is that I get lost and overwhelmed by the fluency and speech cadence of others around me. For example, I know if I take a deep breath and speak slowly (almost like a gentle, calm, sedated person), I will be 10x more fluent. However, this never seems to work in scenarios such as meetings at work since all other folks in the meeting speak at what sounds like 300 words per minute, and they do so effortlessly. This causes me to panic and forget how to breathe. My question really is, how do you not let the way other people speak affect your own speech? I feel weird very strange and isolated when I am the only one speaking so slow and calmly, while everyone else barely takes a breath and manages to speak like their mouth is a machine gun of words. It's also not like I have the right to tell others to slow down or speak differently because of my damn stutter. Appreciate your tips/advice.