Believable & frequent skinship:
It's Okay, That's Love
Too Late To Say I Love You (most realistic sexual encounters I've seen in a drama ever! I loved it!)
They Kiss Again (I see you've watched It Started with a Kiss, I found that They Kiss Again had even more and better skinship)
Mars
Very good, but somewhat infrequent skinship:
Lovers
Aishiteru to Ikketure
Cruel City
I can't say that I agree with the rec of Ugly Alert above. The skinship there was very awkward, think closed mouth kissing, lip brushing, lots of piggy back rides and hugs ... no real kissing, no love making ... BORING!
The intimacy just seemed forced, unbelievable and fake to me. I don't know any pair of lovers who would act like that around each other. But that's just me. Maybe you'd like it although I don't think you'll watch it anyway since the drama is 133 episodes long.