Arduino Wifi + NFC (SPI) not working together

Putting this in the networking SPI section, because I think thats the issue I'm having.

The setup:

Arduino Diamondback (duemilanove w/ wifi adapter on board) - Seeedstudio NFC shield -

The NFC shield has a hard coded SS pin of 10, which I've revised to sit on D5 with a jumper wire (as the wifi onboard uses 10 for SS), and that gets the NFC side of things working great.

The Wifi side won't work consistently though whenever the ICSP pins are connected to the NFC shield, so I think theres some sort of conflict going on. The same thing happens when I try the official Arduino Ethernet board, which also uses D10 pin for SS.

Can anyone point me in the right direction as to how to get these two boards to function together? The goal is to transmit NFC/RFID card id numbers to a remote server over wifi.