You will never see a European apologizing for his accent. Almost 7 years in the U.S, and I still speak very Indian English, neutral at best. My professors always graded me well for presentations, potential clients understand what I say, and
yesterday I had a 2-hour long conversation with someone who shares my passion for women empowerment.
Sometimes, I speak very fast (trying to change that). Recently, I have downloaded an app that helps me to analyze my pronunciation by comparing audio waves with a template. I have a lot to learn. I am taking a course in public speaking to boost my confidence.
But when I look at the videos of successful people of Indian origin in Silicon Valley, I don't see them faking an accent. All I see is their competence, their expertise, their depth of knowledge in their chosen field. And this makes me believe that confidence and articulation comes from a thorough understanding of your subject- you can not fake that.
Update: My friends and family say that my accent has changed organically over the years. I will upload another soundcloud file to examine the difference.