Am I taking crazy pills? What's the problem with just politely saying, "Can you please not interrupt?" or "Let me finish my point please."
I'm assuming this option has already been exhausted and didn't have any effect.
I've worked with people who prefer to apologise all the time instead of changing their behaviour. When you bring that up they... apologise and move on.
I've become aware of that recently because of reasons, and I think it's all right to not just drop it after someone apologises. It's all right to not accept an apology if the underlying behaviour isn't changed.
If it keeps being a problem after that (only in an extreme minority of cases would this be true), then yes, I'd transfer or look for a different job.
But engaging in a war of talking over each other is just stupid and immature. I have kids, so I guess I prefer the workplace to consist of adults acting like adults.
It is actively defensive.
"If you're being interrupted, it's because you're interruptible"
What a load of victim-blaming shit. There are people, and I've worked with many, that would have interrupted Jesus preaching the Sermon on the Mount.
If both parties keep talking it will get awkward for everyone in the conversation. This is what you want, as it will lead to immediate understanding that an interruption happened and that it's not OK. You can calmly discuss afterwards that you were interrupted, and after a few occurrences even those with only a modicum of social awareness will get the message and change behaviour. And peer pressure can then help those stragglers.