As of release 3.0.0, you can now use SerialTransfer with UART, I2C, and SPI. With this update, you can now transfer entire files over SPI. I've even included an examples of how to transmit/receive 2kb files over UART and SPI.
GitHub is down rn, but if you download the current release via the Arduino Libraries Manager, you can look at the file transfer example sketches.
I hope you find it useful and please let me know what you think of it.