I am using the FIFO on Teensy 3.0.
The maximum SPI frame size for the K20 is 16 bits, not 32 bits.
I have not tried 16 bit frames yet since the Freescale examples were a mess. I suspect 16 bit frames could help a lot.
I plan to try DMA in the future.
The absolute limit for SPI at 24 MHz is 3000 KB/sec but I don't think I will get close to that for 4 KB writes, even with DMA.