Director's run unopposed. So they win just by voting for themselves. The C cannot vote on the CEO position (no shares can).
It is a certainty that if C shares are sold there will be a vote scheduled to raise the auth limit. Nobody would buy into the deal without a commitment by management to do so.
I would pencil in more like 2.2B as the new limit. That would give them enough to sell the Cs with attached warrants and a little headroom.