Background video - listen/watch different sources

I'm about to invest in new home theater components and something that would be very important to me is to be able to watch one video source on my television while listening to music from another source from the same receiver and set of speakers. Here's the specific example I'd like to accomplish: mute the football game and listen to a record. Now obviously I only want to purchase one set of speakers that can be used when watching movies or TV or when listening to my turntable or other audio source. This means I don't want to set up a "zone 2" of speakers there in the same room because that would necessitate (as I understand it) a complete second set of speakers. Someone suggested I plug the HDMI from the satellite straight into the back of the television which then means I can't use these speakers to listen any audio from the television programs I may watch (unless I manually switch the cable back and forth, which I don't see as viable).

I have been told (from Yamaha support) that this would be called "Background Video" and that it as a functionality has disappeared from receivers with the prevalence of using HDMI connections to/from receivers.

Obviously I've googled and read reviews and so on, but I cannot find a receiver that can make this happen in my home theater. Do any of you dear forum readers know of such a receiver or likely brand? Or perhaps is there another way to accomplish this other than manually switching cables around or using zone 2 functionality and needing another set of speakers? I would GREATLY appreciate any guidance, thank you.