A few days ago I observed that today's receivers are massive klooges. I hoped in posting that to be shown it wasn't true, and there are exceptions. Turns out at least two brands that have consumer-level products, Denon and Marantz, have receivers that are designed with the reality of HDMI built-in. Their back panels give the named labels to HDMI ports. There are still a couple of RCA type jacks in case you have an old phonograph or reel-to-reel tape around. Here are a couple of examples.
I got an excellent suggestion from John Pettit. Look at the back of the TV set, Mr Dave. Look at all those HDMI inputs. So plug all your stuff in there. Now guess what, there's an RCA output option, so plug that into one of the input RCAs on the old receiver that's powering the great tower speakers. It worked. It took a while to find an input that was right for the output the TV was producing, I think it was the CD input.
All is good except one thing. The Mac Mini apparently isn't putting audio out through HDMI. So the Mac Mini will no longer be a place for me to play videos. Instead I'll go via AirPlay to my Apple TV that does put audio out on HDMI. Now the question is will all my iPhone software work with it. I already found that the Time Warner app doesn't. The crucial one is the NBA app, so I can watch this season's games using my online-only League Pass. With that, and the ability to play videos on the iPhone, and the set top box that's already plugged into the TV, I'm a super happy camper.