So it's more about the form of the conversations, and less about the content?

Basically. But I think the form of the conversations leads to much better content, and more depth of exploration, and clearer / faster communication.

wish there was some way to politely signal the person to make their point quickly and give someone else a turn.

I honestly find that this is difficult. I think it's easier to learn how to politely interrupt, or just be careful about the groups one hangs out in, or speak in smaller groups.

And then when I get a chance to speak, I'd fear that I'm not being as interesting as I had expected to be when I decided to speak up, and other people are thinking that I should stop talking.

That is interesting. I try to keep my points short, when possible. I think short points also facilitates better communication; shorter back-and-forth periods enable people to ask for the specific information they need, and closes inferential gaps.