Mapping MOSI, MISO, to other pins

I am using a Board of Education Shield with nRF24L01+, where there are conflicting pins with pins 11-13 are being used for both the nRF24L01+, and also for controlling the servo. In the end, my nRF24L01+ is unable to receive or send anything at all.

Is there anyway to either map the MISO pins to other pins, or change the pins used for controlling the servo with the Board of Education Shield?

With the Uno (and others using the atMega328) the SCK, MOSI and MISO signals are fixed in hardware and not reassignable. The only solution in such cases would be to "bit-bang" the NRF24L01.

I have no idea about the other board you mention, you'd have to post pictures and a schematic for anyone to provide an answer to pin reassignments.

This is the datasheet for the Board of Education Shield.

On page 6 of the pdf file there is a detailed description of the shield.

The servo control pins are the exact same as the SCK, MISO, and MOSI.

Also, even though I tried to connect directly to the ICSP pins, it worked with the Shield detached, but when I attach the Shield, the transmission failed again.

What about the “bit-bang” you mentioned?

Can't you lift the data pin out of the servo plug (yellow wire), and connect that to a different pin.
Gently lift the plasic lock/retainer with a sharp knife, and the pin just slides out.

Bit banging is a programming technique where by you use code to set and reset pins in order to emulate a protocol.
So you could write a code that could use any pins to talk to SPI hardware.