I think it works as it is, but it just seems to be rather verbose. What you added isn't wrong, but it makes the sentence even more wordy and convoluted. A lot of writers try to avoid saying "being," in a lot of scenarios, simply because it sounds bad. You could add, "with death and marriage acting as the engines of housekeeping," which doesn't sound great, but makes it more clear, and I think it sounds better than "being." That's just my two cents; I'm sure others disagree.