I thought I had a solution for you, but it looks like someone else will have to weigh in.
The Yamaha RX-V575 has a "Zone B" option. With that option, the unit will play 5.1-channel sound in the main zone, and downmixed 2-channel sound (of the same input) to Zone B. This would be exactly what you want, except that Zone B is a speaker-level output only. You wouldn't be able to connect an external amp.
So I checked out the two-steps-up RX-V775, which has a "Zone 2" that is output via RCA jacks (i.e., you can connect Zone 2 to an external amp). However, in the higher up models (and it appears that other brands, e.g., Denon and Pioneer, do the same thing), Zone 2 is meant to play a different input than the main zone. And, according to the manuals, if you select the same input to be played over both zones (called "Party Mode" by Yamaha; no special name by Denon), the main zone (your living room) will play only stereo instead of 5.1-channel.
It's kind of a bummer, since one day I will need this same functionality. Maybe someone else who has solved this problem can share their solution...