My friend and I (who can connect with everyone else, but cannot connect with each other in Divinity and only Divinity) have two different service providers. I have Comcast, my friend has MediaCom.

Note: we can connect using other Xbox's using the same internet sources! We CAN'T connect using the same consoles but with different profiles logged in. We also CAN'T connect when we take the same xbox's to different locations/internet sources.

This narrows down the issue to being only one thing: My XBOX cannot connect to his XBOX and only his XBOX in Divinity, and only in Divinity. Somehow, someway, it's an Xbox to Xbox issue specific to this game.
This, needless to say, is extremely strange. What is it about my Xbox (not internet, profile, server, et cetera) doesn't like his, and only his, Xbox for this game, and only this game?

This is also why you cannot repeat this bug in the game-tester setting.

Note: My friend had signed up for, and has been using the new special dashboard for the Xbox One. However, this have not interfered with anything else, and I can connect to another friend who is also using the same dashboard, ruling that out as a possible cause.