A heroic effort, for which you should be applauded. Misunderstandings of basic measure theory are the cause of many avoidable disagreements.

(0∞, on the other hand, is just 0. We make this definition because, e.g., the area of an infinitely-long-but-infinitely-thin line should still be 0.)

I agree that in many contexts it's obvious what we should mean by 0∞, in a way that it isn't usually for ∞−∞, but not that this definition is either always useful, or universally accepted.