Well, unfortunately I don't have a recipe here for finding these, the landscape is just too big. It basically boils down to finding the right "enchantment" to search for at mouser or digikey and then using the parametric search to home in.
If you want to further reduce BOM count, I think there's also a 16 channel version of the TLC5916. I leave it to you for hunting it down, now that you know the manufacturer and the family, it shouldn't be that hard.
Regarding the high-side drivers, I thought you were doing an LED matrix, and those are usually arranged in rows of which only one is enabled at a time.