As described earlier, I spun a small test board through @oshpark with the same diametre and side-mount LEDs as the final goal.
I've now written a driver for the TLC5947 in C and tested it out. The excellent @Microchip Technology Curiosity board was the closes dev board within arm's reach, so it got the goods. Guess I'm using a PIC for this project! I hadn't decided until now.
It's probably a good idea anyway, I'm more comfortable with the low level peripherals than with the other option I was considering (ARM Cortex M3).
But it blinks!
It's pretty efficiently written, I feel pretty confident in good resolution being possible. As I write this, I realise that I haven't done a full stress test of all the LEDs in the array turning on and off in rapid succession. That'll give me some indication if my voltage lines are sagging. I'll post up the driver code in a bit, too. It's fairly simple.