If pronunciation is your caveat, I would highly recommend singing.
I have had experience with this, myself; although I am a native english speaker, I feel this would still benefit a non-native speaker - especially one that only has problems with pronunciation.
Growing up, I was diagnosed with a speech impediment that grossly affected my pronunciation of words. I went to speech therapists in effort to fix the problem, and it was not until one such therapist introduced singing that I was able to overcome my issues pronouncing words. I had been seeing therapists for the greater part of the year; singing fixed my pronunciation within the month.
More recently, I actually attended singing lessons, in which my teacher found that I was not pronouncing particular words very clearly, due to the song being sung in another accent. They taught me to start off singing in my native accent, while emphasising the pronunciation of words. As practice went on, I quickly found that I could fluently sing the same song in the original accent.
Hopefully this helps, if you wish to adapt your accent for better pronunciation. It is certainly worth addressing the simple fact that your accent is a representation of your culture, and you should not really have to.
Personally, I would not consider it mis-pronunciation if the altered pronunciation was the result of an accent. Assuming you work in a professional environment, this should not be a problem. Furthermore, any negative reaction you might have should tell you a lot more about the other person than it should tell them, about you. This would personally only tell me that you were not a native speaker, and give me more respect for your communication capabilities.
To quote some Aussie slang;
English is a **** of a language