I was idly under the car hunting for things that hadn't been checked yet, and started putting some focus on the control arms, and the bushings. I discovered the bushings are toast, BUT..... after a few tweaks, I drove the car later in the day today and the sound was no more. Ohhhh the silence.
What did I do? I gave all of the control arm bolts an extra 1/8 turn or so tighter, but I also got between an 1/8 and a 1/4 turn on the two bolts that I think hold the subframe to the car? Or maybe they're the bolts that go up and hold the sway bar down tight, I'm going from vague memory right now. There's two, each one nearly directly rearward from the control arm bolts. They're huge, they're either 19 or 21mm, impossible to miss.
Anyway, that fixed my problem. Let me reiterate, my noise was as if something was shifting forward and backward, so upon throttle, it would shift (maybe providing 2-3 pops), and no more upon throttle. Then, upon braking, it sounded like it shifted back to where it was before. Not really on bumps, but occasionally. Not really in turns, but occasionally. If I'm right about the shifting metal concept, that could certainly be happening over certain bumps or certain turns in certain situations.
EDIT: Let me just say before anyone else does, yes, I am the asshole - because I should be making sure everything is always torqued correctly. Lesson learned!