I really like your sheet analogy. But if matter and energy are the wrinkles on the blanket, what does the coffee represent? What does this information consist of if not matter and energy?
Maybe in the alternate world matter and energy are the stains from colored liquids on the sheet. But if that were the case, wouldn't the stains slowly fade back to white, in the same way the wrinkles get pulled out flat in this world?
Further, even if a stain survived the fading process, since it is neither matter nor energy, how would we perceive it? If we can't perceive it is it really there?
It is a nice twist of ideas, but I don't think the coffee part holds up as well as the wrinkles.