So, I made some progress! I decided to mess around with the settings. I was able to mess around on GTAO for awhile and start chatting with some people. I was able to hear the game AND the chat out of the tv, and was not giving off any feedback. As a matter of fact, I asked them flat out and they all said everything was clear, and there was no background noise. Hopefully this will work for RDR2. My settings were as follows:
In Settings/Devices/Audio Devices/Output Devices, I chose 'TV or Amplifier (obviously) and in Settings/Sound and Screen/Audio Output Settings I chose HDMI OUT. (It had been set to DIGITAL OUT - OPTICAL) I think that was one major issue.
In the quick menu, under Sound Devices, the output to audio was actually set to 'Chat Audio' rather than 'All Audio'.
Anyhow, the most important setting was the microphone level. I had it way down, and everyone could still hear me fine and it was low enough that it did not pick up any audio from the tv. The tv was up pretty loud too. So, the only thing left for me is to find a descent headset for October, now that I know how all the settings should be. What a relief! lol