503 Response on fresh install, FastCGI possible culprit
Okay, my next stackexchange question will be "Where is the dunce cap?" because I could use one. My problem was not actually a problem, and Lindsey D was exactly right: I was just going to mysite.com, not to mysite.com/admin.

And I see now that that was clearly stated in the install instructions, a tab that I was referring to over the course of the whole afternoon!

Thanks, Lindsey, my morning just opened up. And to the dev of posterity who finds his way to this question and answer: I know it hurts.