I could have skipped all the ridiculousness... Finally saw reference on another forum to 123.hp. com/setup, and remembered that's where I had been directed after buying and unboxing the printer to set up. This takes your through a complete install and installs the printer in the Printer & Devices folder in Preferences and sets the Envy Photo 7885 as the default printer. What a wild goose chase. D'oh!
Every other avenue I followed did not do this. Sheesh.
Technology is wonderful, but troubleshooting the issues, not so much. Thank goodness for these forums, I swear the best answers come from enthusiastic users who share half the time.
I am happy to report I've printed and will now be getting alerts and stuff via email, so the HP marketing team should be happy.