Conversational turns hand over in a fraction of a second, which is why 'wait for a gap' has never worked for you. Signal before you speak, start as they're finishing, and get back in when you're cut off.
Speakers hand over in a fraction of a second, and the next person starts as the current one is finishing rather than after. A silence long enough to feel comfortable stepping into is one where something has gone wrong.
An audible in-breath, a slight lean forward, a small hand movement. It's mostly unconscious and it's how the next turn gets claimed — and if you're not doing it, you're competing for a turn nobody knows you want.
The point isn't clever enough, someone might have said it already, it's not quite formed. Meanwhile the people talking most are applying no such standard, which is most of the gap between you.
Interruption is patterned rather than random — women, junior people and anyone in a minority in a given room get cut off more. Where that's happening, no personal technique fixes it, and treating it as your failing keeps you working on the wrong thing.