It is important for the board to determine whether or not they agree with their founding values. Since they do, it is now time to say to the employees, "Choose you this day whom you will serve, but as for me and my house, we will serve the Lord." Either you believe what the institution promotes, and continue to work there and teach it, or else you don't believe it, and should find another job elsewhere. This is the direction the board needs to turn to next. Easy? No! Difficult? Yes!!! But, I beg of you board members to consider: Who will you serve? What do you want to have God say about how your influence was used? How will you answer in that last day that is coming soon?
This is not a public institution. Public institutions must be run differently. This institution, while answerable to government for certain things, is ultimately answerable to God. Please pray for His Wisdom, Grace, and Power in dealing with this difficult situation.