Aight, I did get a single strip made. I need to make three more however I may or may not do that. Couple of reasons, as well as lessons learned:
a) I requested 100mm x 150mm boards, 0.8mm thick. I had my board layout tiled seven times and I was prepared to cut them out myself as none of the cheap Chinese vendors will do that for you. Well, as it turns out, something that large, that thin, is prone to warp a little. In fact, they were slightly bowed already when I got them and it just got worse when I reflowed the ICs on one side. It’s not bad, I could still use them. It’s just going to be a tad tricky.
b) Personally, I’m just going to either find a fab house that can cut the pieces out for me, or just waste material (and money) on a single layout on a single 150mm x 50mm piece. It honestly isn’t worth doing all the cutting and cleaning yourself. Again, this too isn’t a show stopper. I can continue with what I have if I choose to.
c) This is what could be the show stopper … I discovered that at 5V, I can push data just fine to the strip. However, at the lower voltages, it gets corrupted. First thing I did was check the datasheet in case I made a mistake. Nope, it says 2.7V - 5.5V (absolute values) so I knew that a 3.7V Li+ was fine. So why the corruption? Tried grounding the DATA and CLK lines at the end of the string. Nope, got worse. Slowed down the data stream, no change. Then, on a hunch, I decided to use a pull-down on the lines. Don’t ask me why, I just thought if the datasheet recommends a 33 Ohm series resistor to the next section (though they’re talking 6m lengths, and I’m dealing with 28.8cm total length) … so why not. So I pulled the lines down with a 47 Ohm resistor (closest to 33 Ohm that I had on hand.) Tada! That solved the problem. I’ve been running 16 images, 15 seconds each, on a loop, non-stop, for over an hour, on a single Li+ battery. I turned it off because my eyes started to hurt - these suckers are BRIGHT. But the board wasn’t made with the resistor pads, so either I get new ones made or I use a standard through hole resistor just soldered onto the board like it’s an SMD device.
d) If you want to do a double sided SMD board, think really hard about it. On this design I have the ICs and capacitors on one side, and the LEDs on the other side. The LEDs are meant to be soldered on manually. But, um, I wouldn’t recommend it. It’s not impossible, but damn it’s a pain. Trying to align them precisely just won’t happen. And I’ll have to elongate the pads a little bit more just to make it easier to solder. Again, it’s not impossible, it’s just a royal pain! But, out of 48 LEDs hand soldered a little less than 1mm apart, I only had 4 of them I needed to reheat with a dab more solder. So again, it’s not impossible.
e) Test displays are showing me what kind of images work best. But it’s also telling me that narrow images need to be slowed down while wider ones sped up a little. I have to come up with a formula that calculates the speed at which each column in an image get refreshed. I need to figure out a “base” number of columns that looks good at a regular speed. Then narrower images need to get slowed down to match that base number, whereas wider images sped up. I know, basic arithmetic … just need to get it done.
And lastly, now that I have a strip made the actual length the end product will be, I can pretend to be swinging them in a circle and take pictures. In reality it’s just on the ground, under the camera tripod with the camera swinging in a half circle. 
But, it gives me an idea of how the images look. Here ya go:
