Being comfortable / Social Awkwardness

I’ve always struggled with social-awkwardness and insecurity. I get very uncomfortable, very easily. I start thinking too much and what if I say something stupid, etc. For example, I had coffee with a new person for business purposes this week. While I wasn’t exactly nervous, I couldn’t stand the lulls in conversation and would just start spewing out words to make it go away-word salad! The one good thing is that I used to beat myself up for it for days and relive it. I don’t do that much anymore. That said, I want to be a more comfortable person.

I also struggle with being myself. I’m actually quite funny and quirky but when I meet new people, unless there’s some unusual instant connection, I usually don’t act like myself. It just disappears! I’m ok with being quirky and different on paper but I do struggle living this out. And furthermore, I quit drinking so that magic ability to expedite this process and be myself around new people has gone away.
Here’s my model for the first one:
C-social behavior
T-I am comfortable
A-casual conversation with ease
R-friend and business connections mad and peace of mind

and the second one for :
C-my personality
T-My personality is worth showing
A-Be myself
R-More connections and friends
So, the reality is that I don’t have that many opportunities to practice these so that would be one thing to do–create more ways to practice. But in the meantime, how can I practice this without being in the actual situation so when the time comes, I can feel more comfortable (or comfortable being uncomfortable). Any tips for books to read on the subject(s) along with doing the model? Thanks!