tails_naf:
Hopefully it will be the end of my reset-related woes!
It was for me! I've had no problems with the reset and the SD since.
I forgot to mention that on the Uno, digital pin 10 is the default slave select as well as the w5100 slave select. Since the SD.begin(4) call sets the default slave select as OUTPUT and HIGH, the w5100 is disabled in the SD setup on the Uno. But on the Mega, this is not the case. It must be disabled by your setup code.