Ok, it's really late (I should have been in bed 2 hours ago - just got done rearranging my SD card for my Wiz!), but I wanted to quickly let you know how I fixed my problem.
So, after some helpful info from MWeston (thanks, you're awesome!), I checked my cable with a volt meter and got the same thing - +5V on pin 16, with ground pins 19 and 12 correct as well (EDIT - I should point out that I was only able to test the voltage at the wire, my volt meter's probes were too large to fit into the plug itself to test the pins directly, so it's unknown where the real problem lie). So I don't know what's up with things - if the Wiz's internal Pin 16 is defective, or just something really funky with the cables - I tried soldering onto another USB cable and that didn't work either, so it's either the cable's prong itself, or for whatever reason this batch just doesn't want to charge with +5V on 16.
However, after checking a pinout, I discovered that pins 21 and 22 on the cable were ALSO inputs for +5V, meaning that technically the Wiz has redundant placement of voltage in. After confirming with MWeston that hooking up more than one of these won't fry my Wiz (apparently his cable is like this) I desoldered the USB signaling wires (the Green and White, for those playing the home game) from their pins and used a pair of needle nose pliers to move the prongs themselves to slots 21 and 22 - it was pretty easy, just pull them down and out and put them back in - just take care not to bend them during these operations, and make sure you retain the facing so that you don't put it in backwards - this shouldn't hurt anything, but it won't work either. Then I threw a big glob of solder across pins 21, 22, and 16, so that the red wire was attached to all three, and the green and white wires were unattached.
Lo and Behold - IT WORKED! I jumped for joy when I saw that little red light turn on on my Wiz when I plugged it in.
Here's the rather large caveats, please read before you bust out the soldering iron.
1: I have no idea if this is a good idea or not. While technically MWeston's Wiz cable is like this, he's probably better with a soldering iron than I'll ever be, and if Pin 16 wasn't working like it should, then who knows what it might mess up to have it soldered like this long term. God only knows what else is wrong here. Just because mine hasn't blown up yet doesn't mean it wont...
2: This disables the USB function of your Wiz cable - for me, I didn't care, I have a USB SD card reader. I can't load things onto the Wiz NAND now though, but I'm not sweating it too much, I'll care more when my SD card is full (16gb - cheap as dirt these days), which it isn't yet. However, if you intend to use the NAND, this is not really a solution.
3: Soldering iron, accoutrements, and knowledge of soldering techniques are necessary. While this is a pretty simple operation with a fairly low margin for error, there is still the potential for you to blow up your Wiz. Don't do this unless you're prepared for the worst and/or comfortable with the risks of getting out the solder and iron. I take zero responsibility here. Test your cable thorougly before plugging into your Wiz - my recommendation is to test with a wall socket AC adapter (I used one for an iPhone, btw), so that you don't potentially blow up a PC if you short the wrong wires. Maybe that's a bad suggestion, but I trusted my house's surge protector to be smarter than the USB ports on the front of my reasonably expensive PC...
I personally am going to try getting a replacement cable from Korea which hopefully will work for charging and USB to see if that will fix the problem without needing an RMA, as otherwise things are working fine. I just completed a full charge and I'm very happy to say that so far it's working great.
Thanks again to MWeston, ED, and everyone else who offered advice and suggestions. If requested I can post pics of my cable for those that want to see, it's not that special though.
I get no LED change. Only LED I get at all is blue, when the unit is on, so clearly it's not charging. I've had it plugged in and turned off for about 2 hours and the battery is still saying it's low.
