Vocal habits are very difficult to change. That's something I'm more experienced with than you might guess, since I studied to become an opera singer when I was younger and also read a great deal on vocal pedagogy.

The problem really is that, in the early stages of coaching, an increased awareness of your own voice production can get in the way, as if you were standing naked on stage, surrounded by mirrors! So you might end up insecure & nervous or else stiff & affected.

Undoubtedly, there are public speaking coaches or even speech therapists out there who could break you down and eventually build you back up. (Some people in Boston or the UK pay to shed their regional accents, which I think is a pity.)

Instead of paying more attention to personal mannerisms, I'd recommend thinking less about yourself. Practice engaging strangers in conversation. Random people behind the counter, at bus stops, taxi drivers, etc. Try to work in a story. If they're not squirming to get away, then you're doing well.

You're not trying to be a disembodied voiceover artist. You're trying to speak to people. Really, what matters is what you're telling them and how you spin the story. Gilbert Gottfried can mesmerize a crowd, and he sounds like a crow mid-strangulation.