Question: Is it okay to repeat words of davening to fit in with the tune?
Answer: R’ Moshe Feinstein (Igros Moshe OC 2:22) addresses the issue of a chazan who repeats words during chazaras hashatz and in the berachos before Shema. He gives examples where repeating the words distorts the meaning of the beracha and thus constitutes a hefsek, interruption. There is a machlokes as to whether an individual may repeat words to aid his kavana, proper intent. Even at times when it may technically be permitted to repeat words, R’ Moshe writes that אין רוח חכמים נוחה הימנו - the sages are uncomfortable with this practice. Repeating the chorus in a piyut such as lecha dodi, however, would seemingly not be problematic.
The Aruch Hashulchan (OC 338:8) defends a couple of ‘chazanic practices,’ including the popular use of a tuning fork on Shabbos. While he does say that it isn’t ideal, he writes that we should be careful not to condemn wide spread Jewish practices. Aside from instances such as repeating shema and ‘modim’ (see Berachos 33b), one should leave the chazan alone.
In conclusion, one should avoid repeating words, particularly in berachos and pesukim. Likewise, in a pasuk with Hashem’s name, such as הֲשִׁיבֵנוּ ה' אֵלֶיךָ, it would be better to quietly finish the pasuk before repeating the words in song.