I appreciate you taking the time to have your say!
As you say, it seems that something was lost in translation when it came to setting out what this intermediary plot is supposed to be.
I like the idea you have of the Infernal Puzzlebox actually being a part of the story, rather than just something that has bonuses magically put on it as you complete content. The Enriched Shadow Ring, for example, changed as it got more unlocks, whether it be by crafting it through archaeology or enriching it with energy from Erebus. Here, perhaps, completing the requirements for a tier unlocks a new face of the box and, by extension, the relevant tier perk. Then, the “completed” puzzle box has something of relevance to the quest finale (I’m not sure what that would be).