Well done. And thank's for the English idiom to go with it.
The sentence "to have somebody for dinner" is not an idiom, but it has a double meaning as well, and surprisingly fits very well as a translation of the German lyrics.
Do you know any other plays on words in Rammstein's music? I myself am not good enough in German to recognize them.
They seem to have a heck of a sense of humour.
I don't know, I never listen to their music. I generally go without listening to music for weeks, and when I do I listen to famous pieces of classical music most of the time.