G.S. 160A-107 states that a change remains for at least 2 years "after the beginning of the term of office of the officers elected thereunder." What if the change is to 4-year staggered terms? Does the 2-year period run from the first or second election?

It runs from the first election. Even those who receive two-year terms in that election are receiving those terms under the amended charter, and therefore the first election meets the statutory condition.