Dear all,
the Ethernet shield is repaired by the supplier and now it works as expected (Link and 100Mbit lights are all up, Web server sketch is working, and I saw my own UDP broadcast frames with Wireshark).
The L LED on this new revision seemingly does not map to pin 13 anymore. Alas, the schematics of this new revision are unfortunately not yet available: arduino.cc is reportedly always late in publishing them :~.
I think I also understood the Mega pin 53 business now. It has to stay configured as an output pin so that the Arduino remains acting as SPI master, but does not need to be connected at all. The SPI chip select of the Ethernet still goes via pin 10, the one of the SD card still via pin 4 as usual. Thus, SD card and Ethernet should be both usable one after the other.
Thanks again for your assistance to an Arduino newbie.
Kind regards,
Sebastian