If she extends the offer and ends up with, say 68% holding, then...

If she extends the offer and ends up with, say 68% holding, then in practical terms this may give her 75% votes at some hypothetical situation. Her decisions will be in the shareholders best long term interest, which I imagine may be quite different than short term interests of the small minority recalcitrant shareholders.
Shareholder Protection can not be invoked to protect minority interest which would impair the company long term future, especially in this situation where the TO is really a rescue operation.
About 20% of shareholders are speculators waiting for opportunity to exit at a small profit or at no loss. This is what makes the game interesting, how will Gina meet the speculators challenge.
She has already won, the question remaining is the cost to get to 80% holding.