I’d turn it into a democratic company.
The board is selected by peers from each division of the company. The CEO is elected for a fixed term in a similar manner.
The CEO isn’t elected by the popular vote, else you’d have someone from the most populous division constantly winning. It’d be a similar system to the College vote in America. You’d have to win the most divisions in the company.
Upon appointment to the company. You’re issued shares. Every year of service you’re issued more shares as a bonus with company results.
Eventually the airline will be owned by the real stake holders. The employees.