I think people get too hung up on the physical Reaper and neglect to take into account their minds. As we learned in ME2 they're more like Geth in a lot of ways in that their bodies are only shells that house a mass of individual consciousnesses (or programs) though while the Geth programs seek consensus from differing viewpoints, the Reapers are at the same time many minds and one; "We are each a nation. Independent, free of all weakness."
For a being like this the body is just a shell, it's the mind that matters. Remember that the Reapers' greatest weapon isn't that molten metal gun or it's barriers, it's indoctrination. A weapon of the mind and even a dead Reaper can continue to indoctrinate. How this all ties into injecting their young with human paste, but I suspect it's something along the lines of imbuing the new Reaper with the collective minds of the species they're "ascending." There's probably more to it than that, but I think that's about the shape of it.