...since I upgraded to El Cap I've apparently lost the ability to connect to the Internet via ethernet and stream music via AirPlay at the same time....
Well, it took an Apple network specialist to figure it out, but all I needed to do was power down my router for three minutes...the "magic number" as she called it. (It obviously had nothing to do with El Cap, which I finally figured out myself [by correlating a complicated series of phone bills, Verizon tech support visits, FTM posts, and OS X receipt entries] about five minutes before she called.)
This is the Apple doc to which she referred.