This has not been answered anywhere else, googled extensively. Only things I found were a few "How to trade" pages, but they're not even in great detail other than some instructions in an answer by Robotnik here: How do I trade with friends over the internet in Pokemon Sun/Moon?
However, I seem to have an issue beyond these instructions. I, and my friend, have followed these instructions to the letter, but cannot see each other in the Festival. We have been in each others NDS's as friends for years and have had no issues adding each other in previous Pokemon games. He has traded with friends in Sun/Moon, albeit locally, but I have yet to due to this issue.
Note: I do see random "passersby" but not NDS-registered friends.