Coming up with a system of purse string deadlines or play selection deadlines, enforced by the school, is a great way not only to get the director to work in a timely manner but also to perpetuate the student-run producing group beyond your individual graduation dates.
However, there is no communication skill that will change other people. There simply isn't a silver bullet or magic spell to impose your will. You can't *make* someone else share your priorities. Instead of trying to get your director/president to change her personality, assume her end-of-semester burn-out as a given circumstance and investigate what positive steps you can take to make the shows as good as they can be under these circumstances.
As a stage manager, I often try to lead people to make their own discoveries. Even if I already *know* what the solution is, I never propose the solution (unless said solution is completely within my power to enact, without depending on others); I try to help my colleagues see the problem and ask them for the solution. In your shoes, after the current show is over, I'd say something like "If only we could have gotten John Doe for the lead; but he took that conflicting class before we held our auditions and couldn't read for us" or "I wish the actors had more time to learn their lines; they never really did get off book" and then genuinely ask "How can we keep that from happening on the next show?" This is the trick: even if you *know* what to do, you have to *ask* completely genuinely, with an open mind, because it is always possible that the person you're talking to, who has the power to enact a solution, may come up with a solution you never thought of but still makes the show better. And it's better to leave that meeting without an answer than to jump in with your own answer; your colleague may need to sleep on it. All you need to do is communicate what the problem is as clearly as you can.
On the upcoming show, instead of dragging your director to a meeting she doesn't want to attend, try approaching her with problems and asking her help solving them. "How can we get enough time to rehearse?" "I would love to start rehearsals with all the props we need, how do you think we could do that?" People love to be heroes who solve problems, and giving them opportunities to do so is what I've based my career on. And if it's in your power to execute or support any solutions she comes up with, tell her specifically how and when you can help with them. Commit to their solutions as strongly as you commit to the show as a whole.
Now, I should also say that I try to keep *my* problems away from the directors and actors as much as possible, as the major problem *they* have to concentrate on is rehearsing the show. But as a stage manager, it is worthless to engage in a power struggle. Leave aside your preconceptions of the way things "should" be done and search for the best available path to opening night given the people you're working with.
Sorry for the long answer, hope some of this was of aid.
