So in your mind, we should reject the assertion that "all human life deserves dignity and respect" out of hand, but continue to live our lives as though that were the case anyway, despite the "fact" that it doesn't?

Yep. Morality, to the extent we need to verbalize it, is all about replacing reality with the right fictions.

it isn't a giant leap for me to realize that it would be objectively immoral for me to terminate the life of another organism arbitrarily.

You can't make something "objectively" immoral by subjectively declaring it so. You think someone else's wanting to be alive imposes a duty on you. I don't. I think my wanting to be alive imposes a life strategy on me that includes not killing others. I may internalize that strategy as morality, and my genes may even dispose me in that direction. But the other person's rights are like the spots on the bowling alley that pros use to line up their shots. Hit the spots, and the pins fall. But the object of the game is not to hit the spots; it's to hit the pins.

As far as I'm concerned, life is the most rare (and therefore precious) thing in the entire universe, and we should be promoting life rather than destroying it.

OK. That's how you get where you are. Others rely on religion. Still others rely on game theory. I think the evidence is clear that humans have some innate moral drives, and that's a good thing. Whether we are just rationalizing them isn't really very important. What matters is that we behave well by whatever rationale works for us.