I am using optical for the ARC. If I understand this correctly...I can output chat through optical? I don't think I ever seen that option on the audio settings on the Xbox. Maybe you're referring to "output chat to speakers"?.
Yes, I meant output to speakers.
Settings > General > Volume & audio output > Party chat output - set to speakers
If you find games are too loud to hear chat you can change your chat mixer settings here too.
I did try that setup on the diagram( the one with the splitters on both the ARC and chat adapter and I was getting echo. I however didn't see the part where you mentioned to eliminate the green lines on that diagram. I would imagine it is pretty much the same thing as just plugging in the Y splitter off the headset to [ 1 ] Headphone to ARC and [ 2 ] mic to controller input. Doing that still have my party echo on their end. This is so frustrating.
Okay, lets try something different. What happens if you change game chat to go through optical and remove the headphone to ARC? I'm saying connect only the mic input to the controller and see if they still get echo. Similar to my modmic diagram, like this:

Still echo? Try jumping past the ARC completely like this:

If you or your friends still get an echo on both these setups, I have to believe the issue is the shared ground sending feedback to the mic. If that's the case, you can either pursue isolating the chat line with other equipment or just jump to a separate mic to brake the loop. For my setup, I picked up this Modmic which seemed to be the cheapest plugin option:
https://www.amazon.com/dp/B075RGBFDY/I just got it along with my AD700X headphones this morning. Two issues with this that make this a bit of a clunky solution:
1) Cord on the headphones is really long, about 2 meters/6 feet longer than the Modmic. Not an issue for me, but if you need the extra length you'll need an extender for the mic.
2) Modmic instructions advise not to attach to mesh surfaces, however, the entire outside of the Audio-Technica's is mesh. I will try it out and see if this is a problem, worst case I'll have to use some stronger adhesive.