My wife says there is no topic too trivial that I cannot over think it.Well that was an awful lot of information in one place. LOL
To answer your question, I have only seen it called Double-line Reefing or Slab Reefing. You can see it discussed in this article: Offshore Sailor: Mainsail reefing Slab reefing used to only mean double-line reefing, or reefing with a tack hook.By the way is there another name for 'two line reefing?' I have looked it up on youtube trying to picture it, but can't find any examples, only normal reefing and single line reefing.
With the popularity of modern single-line reefing systems (with a shuttlecock or balancing block) , the term 'slab reefing' has become too generic for my taste. I know that there are folks who love their single line reefing systems, but I am not a fan mainly due to the higher line loads, more moving parts and chafe within the boom where they can't be inspected, and a whole lot more line to handle. But I also do not like that you cannot make independent halyard and outhaul sail shape adjustments with most single line systems.
I don't know if its still there but there was a Youtube of me reefing my mainsail in a Vlog from perhaps a decade ago. It was filmed by a person that I had helped find a boat. He was filming me so that he would remember how things were done and then chose to put some of those videos up on Youtube. I think he used my full name but may have used Jeff_H.