Korean work visa inquiry

Hi gang, I am relocating to Korea for work and there has been some confusion on what type of visa I should be applying for. I am a female US citizen, but both my parents are Korean citizens living in Korea (mom has US green card). I had dual citizenship until 2008, but renounced my Korean citizenship due to the older Korean laws of not being able to hold both. Originally I thought the F4 visa was the right route for me, and while the official language is not crystal clear on the requirements, it sounds like I would not be eligible with Korean national parents. They are not looking to renounce their Korean citizenship, so which visa am I meant to apply for if I'm looking to work in Korea for about the next 3 years. Thank you in advance for any insight! e