At first glance, the TLC5940 seems quite nice. It offers 16 output channels, each with 12 bit PWM and a 6 bit current limit. Unfortunately, the chip doesn't have an oscillator and when one PWM cycle ends, it needs to be retriggered. This is kind of annoying and it partly defeats the purpose of using an extra chip for PWM. It means that you have to supply a jitter-free clock for PWM and you need to count cycles and retrigger the chip via BLANK when necessary.
I wanted to get it working quickly, so I devised a hack. By capacitive coupling OUT15 to BLANK, the rising edge of OUT15 at the end of the PWM cycle became a positive BLANK pulse which started the next cycle. I used a 4.7 kohm pullup at OUT15 to create a signal there, a 22 nF capacitor between the pins, and a 100 kohm pulldown at BLANK. At BLANK, I also added diodes to the power supply rails, to clip the signal. I'm not sure if those were needed.
I never checked to see if the signal was within or close to specs, but it was perfectly reliable once started. To start it, OUT15 had to be set for the desired length of the PWM cycle, and BLANK had to be pulsed high. Sometimes, it started by itself, but that was unreliable, especially because the initial contents of TLC5940 registers are undefined.