Thanks for the info, Till.
Does the snippet you provided go into the ISPConfig nginx configuration template? Or somewhere else?
If it goes into the template, I assume that the settings will apply to all vhosts. I need to change the hard-coded SERVER_NAME for each vhost; am I out of luck?
This seems to work, regarding the SERVER_NAME value being generated dynamically:
fastcgi_param SERVER_NAME www.$server_name;