If that's not fast enough, you could change hardware to a CPU that has more than one hardware SPI port. You can get "official" Arduino software support using the same processor that's in the Arduino Zero and the Adafruit Feather M0.
You just saved me a bunch of panic. Been working on a long project that requires sending fairly sizable data logs from a SD card over a RFM69. Been working on the hardware, storage, and comm flow over USB, and was just starting to integrate the radio. Everything I was seeing pointed to a big problem using the radio and the SD together. Phew!
Now if I can just understand how to migrate from wired comm to using the radio ... Strangely, I'm having trouble finding examples of doing this with multi Kb files. I would have thought it would be a heavily discussed topic. I'm looking to understand data structures better to see if that's my path.
bo