Hi,
Yes, the CPOL/CPHA setting is not related to the /CS signal.
For the CPOL/CPHA setting, the CPOL only controls the polarity of the SCK clock. For the CPHA bit, when the CPHA is 0, the first edge of SCK latches the data, When the CPHA is 1, the second edge of SCK latches the data pin.
I copy it from the section 22.7.1 Operating modes: clock and phase selection from UM10850.pdf.

For your issue that the slave spi transmits duplicate bytes in high sck clock frequency, I agree with you, it is possible that the spi clock is too fast. For the LPC541xx, when the interrupt frequency is more than 1MHz, the core will be overloaded, maybe some of interrupt is missed. I suggest you use SPI FIFO mode, you can write the FIFO with multiple bytes in one ISR, which will save the core load.
BTW, I do not know if you use SDK driver, the SDK driver is inefficient, if you requires maximum transfer rate, I suggest you write the spi register directly without using SDK driver.
Hope it can help you
BR
Xiangjun Rong