This has been bothering me for a while. There is a major error in one of your rulings, I believe.
The above states that:
Q: How do doubling worlds work?
A: The damage multiplier works as thus: The first “Fire” is doubled to 8 damage, the second “Fire” damage tripled to 12, and the third quadrupled to 16.
This is incorrect. The worlds that double magic simply double all magic damage from each card played, regardless of how many you play. Playing 3 fire magic cards would simply double each one to 8 damage apiece. There is no special effect for playing multiple magic cards.
The phrase "For each additional doubling effect used, the multiplier increases by one" refers to the interaction between (for example) the world and Sora (Wisdom Form). The world says to double damage, and Wisdom form does as well. This means that you are now using two "Doubling effects," therefore instead of the damage being double doubled (Quadrupled), it would be tripled. Thus, a Wisdom form Sora playing a "Fire" magic card on Wonderland Level 2 would deal (4 x 3) = 12 damage with that card, not (4 x 2 x 2) = 16 damage.
If there is an official ruling to the contrary that I am not aware of, I would appreciate clarity on this. I do believe, however, this was the ruling from Jaffer and Rob several sets ago.