I submit that it would be very nice to have a method other than verbal interruption that explicitly communicates to someone that you want them to stop talking. (Possibly an array of methods, depending on why you want them to stop.)

I agree completely.

make it a little clearer that it's a rude thing to express and encourage saving it for cases where it's actually important for conversational flow.

I have been interrupted exactly twice in this way; I appreciated it and did not find it rude. (Particularly helpful was accurately thinking of the signal as "talk about it later" rather than "don't talk about it") The conversation in question felt atypically effective and pleasant, although only a tiny part can be attributed to this strategy.

I would rather such signals be used whenever they save time and further our shared values. If there is any chance, I would be happiest to participate in a culture which could work around human nature to deal with similar problems.