Hello my good friend! I've cracked the case! I shall document the solution to our looping-related woes here so other unfortunate souls searching for the solution can find it!

To Loop, you have to sit down at a lunar sanctuary and turn off the campfire, which will spawn the lunar gambit item. After this, defeating the moon lord will open a portal, which you can travel through to loop!

See this video from the mod creator for more details: https://www.youtube.com/watch?v=zYdo3IKvxZA

Best friend ever! Everyone needs a friend like Joe!