Be sure to watch The Player. In my mind the director is the "manager" of the film's production and it sounds like the producer role being pitched for is probably a line producer role. A line producer has to arrange things, solve unexpected problems etc. Both roles require you are able to deal with people in a mature manner. Don't forget that a good presentation can also be visual - take your concept art or collection of montage to help people understand what the frack you are talking about.
(one of these days I'll take my own advice ...)
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