Guys, I have to admit. I'm an idiot.
I tried every cable I could find to charge these things, no dice.
My wife bought me a new controller and a dual charging dock for my birthday, and I put the new controller on there to charge. All is good. I figured the dock looked dumb with just one controller on it so I put the "bad" controller on it as well and the motherfather started charging.
Dug around in our cables bin and found another random cable, stuck it into the 2nd USB port and connected my headset and that damned thing started charging, too.
At the end of the day, the mini-USB that charges my robot dick and my old work phone won't charge the PS4 stuff. And neither will the Rocket Fish cable that charges my old earpiece. But sure as shit, some random stubby Mini USB cable I've never seen before charges like a champion.
Thanks for the advice y'all, I'll keep it in my pocket for the future. In the meantime, I'm gonna download Ark and take a stab at it before bedtime.