I agree with Yaakov Ellis's answer, and indeed deliberately repeat where the song calls for it.
All of kabbalos Shabbos is a "recent" kabbalistic innovation. And there was a great outcry when they instituted it, adding on to the tefillah constructed by Chazal. As a result, to assuage those concerns, there are various kulos associated with it. For instance, that they say it from the middle of the shul, by the bima, rather than at the amud. Or that a katan can lead it.
To then turn around and treat it as davening, such that one goes to great pains to avoid the repetition, seems "off".
Also, if one is going to be makpid on this, then one should ideally not have chosen a tune that was built with the assumption of indeed having a repetition.
In terms of the point raised in the comment section, about repeating words rather than a whole passage, I am not aware of any part of Kabbalas Shabbas (or a tune for a part of it) that has one repeating just words, such as Boi v'shalom ateres ba'lah ba'lah", which makes for nonsense. The closest I know of is from elsewhere in davening, like Baruch Shenatan Torah, Torah; or uShemo, uShemo, uShemo, echad.
But let us say it did exist. (Update: It does, and Menachem gives examples in the comment section.) There are two points that could conceivably be made in favor of such a repetition.
One would repeat it only if there was an existing niggun which prompted this repetition. And as much as kabbalat Shabbat is a recent minhag, so too the tune together with the repetition it assumes is a recent minhag.
Does repetition indeed make for nonsense? Consider the following English lyrics from "Sesame Street":
Can you tell me how to get...How to get to Sesame Street?
Does the listener really think that there are two questions, one how to get, treating "get" as an intransitive verb, and the other as how to get to Sesame Street? Does the listener become confused and think that the song is nonsense? Or does he understand it as part of the structure of the poetry of the song?
Through the ages, Jews have written piyutim conforming to Arabic poetry, or put it to tunes from the general culture. Repetition of words, even where an unthinking person would believe that the result was nonsense, could well be treated as something of this sort. So yes, "Boi v'shalom ateres ba'lah ba'lah" is saying "Come in peace, adornment of her husband; her husband." But normal people hearing it in the context of a song will understand that the repetition is stylistic, and still make sense of the words. Absent a desire to ritualize it such that each word must be said once, yes, I think it may be plausible and acceptable to repeat words.