With the amount of information you provided, I will not assume to know the exact answer, however, I do have a few questions that can perhaps point you toward the right direction:
1) Have you brought this specific issue up in a meeting where everyone is present? Not alluding to it, but specifically bringing it up (for instance): "I feel that there's a serious issue that may impede our team's success, here's where I think the issue is..."
2) You described the loud/big talkers (LBTs) as very confident in their idea and others might buy it--are you the only one who feel that way? Have you talk to the other team members individually?
3) Have you talked to the LBTs individually?
4) Why do you think the LBTs are always interrupting you? Are you being precise when you talk? Do you bring data that backs up what you say? Do you talk very slowly?
5) Do you ever get good results with a 15-people brainstorming session?
6) Do you feel like you have to be with this group? Is moving on an option?
There are 2 books I really like:
Mindset: The New Psychology of Success by Carol S. Dweck and
Getting to Yes: Negotiating Agreement Without Giving In by Roger Fisher, William L. Ury and Bruce Patton
Perhaps you might find the reading to be helpful to you as well.
Good luck and be happy,
-V.