It depends what kind of character you inherited.
Since I am not certain how your brain works, I can merely share my own experience, which may or may not help you for an answer.
If you ask me how to pass the speaking section of an IELTS test, I would probably persuade you to spare more time on the listening part, that is, you may try to temporarily forget your 'old' accent, and melt yourself into the sound and rhythm of the scripts read out loud from the tape. In this way, you may improve your pronunciation and catch up with the script’s pace.
However, if you ask me how I learned to SPEAK English, I would say "it is a different story." Genuinely, I didn’t really speak much until I fostered up my writing skills. I am a person that has more intimacy with math rather than a language. I need pen and ink to clarify the thought. I need to see how differently it may look, if I arrange the words in another way. Extensive imitations through ‘listening to the tape and repeat’ doesn’t work so much for me, for I would not use the structure of their conversations if I don’t like them.
It sounds paradoxical, but as for me, learning how to write is rather essential for uttering my own words.;-)