On the topic of Reaper soulessness, I think that the Reapers are at least as "peoply" as Legion is. They use metaphors, have some emotional displays (mostly arrogance), and they develop a relationship with Shepard that very closely mirrors Legion's (I doubt Harbinger has data available on why he is so obsessed with Shepard, so to speak)
As for the topic question, what does Harbinger mean when he says, "We are your salvation through destruction"
Copied from another thread:
My personal theory is that one race long ago looked back at galactic history and saw that there was a cycle of destruction, as one race after another rose, warred, conquered, and was conquered (think of the nations on earth). Each time this happened, a great deal was lost forever. Cultures, biological tricks, technologies, psychological outlooks, religions, all destroyed completely. But there was an upside to this cycle, as from the ashes of each civilization a new one was born, with its own unique advantages. The race that would create the first reaper came to dominance, looked around, and decided to take their opportunity to change the way the galaxy worked, farming and preserving the uniqueness of each new race (by transforming them into reapers), reaping just as the races of the galaxy reached their peaks, before they were forced to war with and destroy one another.
So by destroying nearly everything that makes humans human (such as our individuality) they save some elements of who we are (technology, specific proteins in our brains, elements of our culture, et cetera)