Here are my faves that aren't on your 'Completed' List yet:

Move to Heaven: https://mydramalist.com/49231-move-to-heaven
Defendant: https://mydramalist.com/19684-defendant
Prison Playbook: https://mydramalist.com/22624-wise-prison-life
Wok of Love: https://mydramalist.com/28256-greasy-melo

If you like a specific genre, you can check out a list I made with my favorite dramas sorted by genre, see if you find something you'll like!

Favorite Romance Dramas: https://mydramalist.com/list/32Ajxb5L
Favorite Non-Rom-Com Dramas: https://mydramalist.com/list/LAlp6Kz1

Hope this helps!

Coffee Prince - (not set in past but is older drama so... but verrrrryyyy good)

A Gentleman's Dignity - a bit of a more mature romantic comedy

Twenty-Five Twenty-One  - currently airing and set in past but is the best drama I have ever seen. Personally don't care for dramas set in the past but this one hits different (hopefully the ending doesn't screw that up)

  • +1 Twenty-Five Twenty-One, also the best drama I've ever seen, set in the 1998
  • Eulachacha Waikiki
  • Prison Playbook
  • The Secret Life of My Secretary