Typically the liaisons handle communication initially, but at a certain point, often around two months before the convention, the head of programming becomes one of the people dealing with them directly, keeping the liaisons in the loop. Thinking back, it has worked well when I've seen this done, and I can think of one example where this wasn't done that worked out spectactularly badly.

Brainstorming works for generating ideas; I haven't seen a brainstorming session contribute much to actual scheduling. Confusion might be small enough for the schedule to be simple enough, but often the schedule is fairly dynamic leading up to the program book deadline.