When I returned to the waiting room toward the end of the session, I heard laughing several times. They hugged when we left.
They seems happy with how the meeting went. They said they hadn't decided what sort of relationship they were going to have, but I was no longer to be an information conduit between them. Apparently they both ended up with wrong information about each other's wants. I am not at all surprised about that, and not being in the middle suits me just fine.
It's going to take me a while to process all this, but I'm getting an inkling of just how much it has been bugging me on a not entirely accessible level for a very long time now. I am hoping that I will feel lighter and relieved of a burden. I have been in a pretty dour state of mind.