Massive Parallel SPI

I think you will need to use a microcontroller with native USB at the very least like the Teensy (and ATmega32u4 variants)/Maple

This way you can cut out the FTDI latency/bottleneck. I believe from there it should be easy to write a sketch on your microcontroller that reads in a bunch of data from USB and writes it out to the LEDs and buffers the next frame with any spare time it has.