Many thanks SurferTim!
Good try 
before entering into debugging the actual NFC library. Unfortunately the outcome of your code indicates that the issue appears within the NFC library code.
I think that we can stop the debugging for a while and see if somebody else has experienced similar issues with other SPI shields when used together with the Ethernet shield. That can give a hint about where the culprit is.
With disjoint SPI PINs:
Checking NFC...
Start NFC read
Found 0 tags
End NFC read
With shared SPI PINs:
Checking NFC...
Start NFC read
End NFC read