Mmm. I've not seen that much noise induced by SPI. I do though use series terminating resistors at the source of SPI signals to take out the high frequency content of the square waves they produce (i.e. slow edges down), and to prevent any possibility of under and overshoot which can cause momentary current spikes if they are clamped by the substrate diodes. That means 56R or 100R series resistors close to the MCU for SCK and MOSI, and 56R or 100R close to the MISO of the radio.
At low signal levels when permanently receiving though you are going to need timeouts from RSSI to address match, and from address match to payload ready, and reset the receiver accordingly.
BTW I did a quick experiment to check this, I had a transmitter sending alternate packets. The first packet was at the correct frequency and correct sync word, the other simulated noise by offsetting the frequency by 20kHz and flipped one of the address word bits so the receiver got an RSSI but no address match. Result without timeouts was 85% packet loss (AFC kicked in for the noise packet and didn't get reset), but with the timeouts version the packet error rate was 0.5%. That's pretty conclusive!
Mark.