No need for optical connection.
keep the optical connection
In the scope of the OP's question, you contradicted yourself.
OP always had 2 sources of programming: Cox or Netflix. However, the audio format was different per source (Stereo vs. Surround respectively). For Netflix audio to the AVR, OP always needed the optical.
I agree with your original suggestion to use the AVR as the HDMI switcher. Meaning, connect all HDMI to AVR to let AVR do all audio decoding and steering.
The original problem was no Cox Surround with the following connections: 1) Contour > HDMI > TV 2) TV > Optical > AVR
The reason is some TV sets will not forward Surround from an external source (Cable Box, Blu-ray, Media Server). However, if the source is internal to the TV (ATSC, QAM, App), the TV will forward Surround. The OP fed TV with Cox via HDMI; however, TV could only up-channel 2-channel Stereo to AVR.