You can build a modular chassis from Extron using (5) 4 RX fiber input boards receiving signal from hdmi fiber transmitters that have local output as well. Then just a single 4 output hdmi board to feed 1 to the display and 1 to the avr. Could also use another output to feed the house system for viewing.

Still is gonna cost the client at least 100k msrp just for the switching system, but would be the most solid 4K distribution system.