I'm on an E-7 visa with a Master's degree from a Korean university?

Yes, this is one of the most common paths. With a master's from a Korean university plus an E-7 job, you usually score well on the F-2-7 points system (age, education, income, Korean ability via TOPIK or KIIP, etc.), and you need to reach the threshold (commonly 80 points). Lots of people switch this way once their income and TOPIK level qualify. Apply at immigration with your points evidence, and use the official points calculator on HiKorea to check your total before booking the appointment.