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I agree, it's not as great as other war songs.

Кто забыл? Мы даже не пытались вспомнить, ведь автор попросил перевести конкретные песни.
Самая известная, все-таки, "Священная война".

I'd translate simply:
"But the tune will get him even there
And he'll dance his way into the grave"

Here is a continuation of an allegory «"Katyusha" (launcher) firing rockets - Katyusha (girl)...