Improv classes, journalling, listening to good conversations on interview podcasts...
Toastmasters is for public speaking, which doesn't seem quite the same. From what you've described I really get that imptov techniques in particular might help you bridge the gap you're struggling with between your thoughts and getting them out in time. I also think that writing, talking, or thinking out your thoughts and feelings on some popular or favorite subjects could help. I know for me, the people who have been most impressed by my conversation skills have happened to bring up a topic I have studied and thought about a lot on my own. I have so many ideas that if I think them up right there, it is hard to describe. But if I've taken the time to intellectually explore the subject beforehand, I already know how to express the ideas and how to segway between different points more smoothly.