[GenXer]

A new receiver is the most elegant solution. I have everything input to receiver via HMDI (X box, Play Station, Blueray, Apple TV) then output 1 to TV with HDMI and output 2 to projector. I also have a Toslink from TV audio out to receiver so I can listen to my TV in full stereo. I think my receiver supports ARC as well but not sure if it's sending surround signal back to the receiver so I just left the fiber optics cable there just in case. Then it's just a matter or selecting output and input from the receiver.

Make sure your TV, HDMI cable and receiver can accommodate HDCP 2.2 and HDR 2.0 otherwise they won't play nice with each other.