It's been a long time, I don't know if you remember me.
And indeed this kind of drama is rare in K-Drama.
I took the trouble to go to your profile that helped a lot since there is a link to your list of dramas you already watched.
So here are my recommandations:
Thank You - a bit of romance with Gong Hyo Jin, not much the main topic is about the heroine's daughter, who is HIV positive and their lifes since I saw you like 1 Litre of Tears, I thought maybe you'll give it a try.
Giant - not that much of skinship either but a mostly solid story and romance on bord.
City Hall - some Skinship, as there is Kim Sun Ah in it
Can't Lose - about a marriage on the edge, because of miscommuncation and a way to work on it
Love Marriage - not that dusty either on the skinship part, not as juicy as INR though
My Husband's Woman - dramatic since the woman's best friend is stealing the husband.
Hope there is something in the "pot" you'll like^^
P.S.: A Wife's Credentials - I really liked that one, the story is serious, realistic, and due to that there is not much skinship, but the dialogues and everything else - a well done drama