What are the benefits of switching from an E-2 visa to an F-2 visa?

I have been working as a public school teacher in Korea for three years. I have now qualified to apply for an F-2 visa and have achieved a score of 85. I expected that switching to an F-2 visa would allow me to legally take on other jobs in addition to my main work, but the public school contract states that I cannot have other sources of income. Is there a way to amend the contract to allow for part-time work? Also, I plan to continue working at the public school next year, but it seems difficult to renew for more than a year even if I receive the F-2 visa. In this situation, I am curious about what practical benefits there would be in switching to an F-2 visa. I would appreciate your advice.