Conflicting Conversational Styles

I'm quite introverted. I like there to be moments of silence in conversations for reflection and peace. I like to be able to look someone in the eyes and be comfortable without thinking of what to say next or how to reply. When I do think of something to say, I like it to come from that place of silence. When I'm speaking to people who talk a lot and don't need breaks or to slow things up, it gives me a lot of anxiety and it fogs my mind, and I begin hating that I can't be myself. I imagine it lowers my charisma significantly too.

What is the right approach in this case?

I'm hoping to hear something other than "avoid them".

Sounds like you're a normal person. Nobody likes to sit there and listen to someone blather on. Someone not pausing to incorporate you into the conversation is simply speaking to you and not with you.

I am somewhat like you. I often prefer the other person to do most of the talking anyway.

At some point it does become tiresome. But as an introvert, sitting with another introvert who doesn't talk gives me anxiety.

This the perfect time to interject with something.. For example: "that reminds me, did you see xyz on the news about that?". In other words segue into something to break the onslaught of being talked at. Or excuse yourself for a moment with "I'll be right back" and then go in another room and take a deep breath, then return and start a different subject.

When I'm speaking to people who talk a lot and don't need breaks or to slow things up, it gives me a lot of anxiety and it fogs my mind, and I begin hating that I can't be myself.

If I were to say something it'd just be more bull. Taking myself out of the environment is a good shout but then that's got its downsides and I wish I didn't even have this reaction in the first place.

I've trained myself to tune out periodically and tune into a mantra I use that calms me, "I can have peace inside my own mind."

Externally, nobody can tell that I go there. I make all the faces of an active listener, and I smile a lot or frown when appropriate, but I grab my own focus for a few seconds, as many times as it takes. I do this repeatedly during my exposure to crowds or with noisy friends. It's taken practice through quiet meditation when I'm alone, so it's like riding a bike. I get on it whenever necessary, and I tap into it instantly.

This is my reminder that nobody can penetrate any private walls I wish to put up. It allows me to claim my own headspace whenever I wish, and it keeps me functional without anxiety. I often push this mantra 'through' my whole body to relax me. I breathe out any anxiety vibes that may be building, and I fill my lungs and my body with peace.

During hectic conversations where I'm asked a question, I respond, "Hmmm, let me think about that for a moment." Then I pause, and I either respond as I wish, or I've allowed someone else to run over the pause and take me out of the spotlight--which is often my intent. Sometimes I like to just relax and observe rather than get caught up in a verbal frenzy, but when I say something, it's deliberate and usually carries the desired effect.

Consider where your anxiety comes from. Keep drilling until you reach a point where any given outcome doesn't really matter to you nearly to the degree you might auto-imagine. Since your imagination is what causes the anxiety, you can either choose to assign that to frenetic people, or you can work it through to learn that your silence is your decision and there aren't any consequences you can't handle. Once you can grasp that, it takes the edge off of your interactions, and you adopt your own power rather than assign it away to any clumsy people you don't really care that much about, anyway.

Head high.