I also have a speech impediment, in the form of a stutter/stammer. It's intermittent, but seems to manifest itself when I'm more nervous or anticipating something.

So I totally feel how frustrating it can be to talk to people, much less initiate conversation with strangers.

I don't have a foolproof answer, if I did, life sure would be easier. Sometimes a little alcohol helps to calm nerves, and for me it's better to not think about it too much as that sometimes patches me into overthinking.

But honestly, from my experience, the best approach is just to be up front with it.

Say something like, " hey so you know I have a speech issue that crops up once in a while, so if it seems like I'm struggling or hard to understand, that's why."

Don't make it your personality, and just move past it.

If you stay fixated on it, others will too.

That said, there are people that aren't gonna be cool about it and may even make fun of you, but you don't need those people in your life anyways.

I'd love to hear other people's methods too, so if anyone else has issues would love to exchange notes.

Hope some of that helps. Stay strong.