I recommend Sejeong-dong Seoul Bareun Dental Clinic.

On weekdays, there is usually little to no waiting time even if you go without a reservation, but on Saturdays, there are always many people, so even with a reservation, you need to wait at least 30 minutes. While long waiting times are a downside, the medical staff provides very friendly care.

They provide only the necessary treatment without over-treatment, and they do their best to save as much of the teeth as possible and treat them.
And I appreciate that you print out the cost details and provide an estimate, as well as carefully check if any insurance-related documents are needed. Most dental treatments are non-covered, so there are very few parts that can be reimbursed through actual expenses, but I still really appreciate you preparing the documents :)