Bump and a follow up:
Bypassing the Mini and going straight to the router gets the receiver on the network. I checked the firewall on the Mini and it is turned off. I have since noticed that the receiver shows up in iTunes for AirPlay when connected to the Mini by ethernet. I don't know if that means anything here...
The receiver is using DHCP. The router's LAN IP is 10.0.1.1; the Mini's IP is 10.0.1.2; the receiver's IP is 192.xyz.2.2.