I think it's misleading to suggest the two different meaning are simply "the" American and British usages. I'm sure most competent speakers on both sides of the pond are perfectly well aware the word has both meanings (and has done for centuries).
It's true Brits normally use it to mean lasting for a moment, as opposed to Americans normally using it to mean about to happen in a moment. But we all transparently understand the other meaning when we encounter it - and context usually makes it abundantly clear which is intended. Only pedantic Americans would fret over "The display flickered momentarily", and I disown any of my fellow Brits who would take issue with "The dam will burst momentarily".
The good folk over at Merriam-Webster love taking side-swipes at such pedantry. They devote nearly a whole page to this one word in that link, and it seems to me every other paragraph takes a pop at anyone claiming it (or indeed any other word) can only have one meaning.