Setting the pinMode also sets the output hard LOW. That activates the chip select. You can do a digitalWrite HIGH before the setMode and perhaps a delay after initializing.
For all Atmel chips (AVR and SAMD) it is okay to set a pin HIGH or LOW before setting that pin as OUTPUT.
Doing simultaneously I2C or SPI seems strange to me. I don't know why.
DMA combined with SPI, now that would be awesome.
I think some work has been done for the Teensy: GitHub - crteensy/DmaSpi: DMA SPI for the Teensy LC/3.0/3.1/3.2/3.5/3.6
The Teensy has more libraries that use DMA, I have not seen it for the normal Arduino boards.
Some processor speeds:
Arduino Zero: 48 MHz, 32-bit ARM Cortex M0+
Arduino Due: 84 MHz, 32-bit ARM Cortex M3
Teensy 3.6: 180 MHz, 32-bit ARM Cortex M4F (with floating point unit).
Have you told us yet what kind of accelerometer it is and what your project is ? Perhaps there are other ways.