What is the receiver being used for?

Typically a Sonos home theater connects as follows:

• Sonos soundbar (Arc/Beam2 or Ray) with surrounds and/or sub bonded to the Sonos Soundbar.
• In your case it would be Sonos Arc (connected to TV ARC or eARC port via HDMI) with 300’s x 2 and sub bonded to Sonos Arc.

A Receiver is typically used to send audio from a connected component such as a turntable or CD player to Sonos speakers by connecting a Sonos Port to an available RCA-Out on the Receiver.

If there are speakers connected to the receiver you can stream Sonos music to them via the Port connected to an available RCA-In on the Receiver.

The Port can be connected to the receiver via its RCA-Out and RCA-In ports simultaneously 

As of today, I was hoping to use it basically as an HDMI hub. All my stuff is already connected to it, and it has more HDMI ports than my television does. I was hoping to keep all of my non-speaker electronics plugged into the receiver, and have all audio/video flow from the receiver to the TV to the Arc. Is the only possible solution to plug all of my other electronics into the TV directly?

If you want to use your receiver as hub connect the Receiver via HDMI and select that input on your TV when using a device that is connected to the receiver.  

For example: In my setup my AppleTV is connected to HDMI 4 on my TV. I must select HDMI 4 and then video is shown on screen and audio goes to my Arc. *  In theory that should work. However, there may be some conversion process in the background that is negating the end result we seek.

Note: My AppleTV represents your receiver.

 * My TV supports automatic (HDMI) switching when I power on my AppleTV so no need to manually select HDMI 4.