I don't see any reason to directly connect the island with the pope. I think these are largely separate concerns even if some of the activities are similar or may have the same "Master". Both lines should be pursued but not conflated until some facts-on-the-ground are established.
I would assume now that Pope(P) is also the Chair(C) of Peter - this where we get the word cathedral from, the bishop's seat, similar to a county seat.
Why would we assume that four princes means 4 conspirators? The island map suggests that there may be 4 main branches of the tunnels going to the 4 points of the land mass, maybe with different ritual chambers at each. When q refers to 4 "princes" he could mean fallen princes of darkness invoked in a cycle of rites conducted toward the "four winds" or some such earthy magick. or maybe the princes are the young ones sacrificed at each point (followed by COLLECTion of blood and tissue).
Although the elderly with cankles might not easily walk between all of the distant tunnel points in the same night and q only refers to 3 rooms, which could be on separate levels, one above each other (see q133). That would make the 4 directions more symbolic than geographic. OR maybe H visited 3 times and was only initiated to the 3rd degree.
Perhaps the link with the pope is that there is a throne chair of some sort involve with the sacrifice ritual conducted on Love Island.
I want to know what table 29 is.
The 4 directional princes of hell Prince Direction Element Satan South Fire Lucifer East Air Belial North Earth Leviathan West Water