I'm in the same boat as you, I hate the fact that in dramas they can be so in love with each other, and even finally end up together but the most they do is that kiss where they just press their lips together, god. In real life you'd want to grab them and touch them idk.
Anyways the most skinship, or at least the dramas with my favorite kissing/romantic scenes of ALL TIME:
1) A Witches Romance; really really good. You WILL fall in love with the guy.The kissing is fantastic and there's a awesome "romantic" scene which in the first couple episodes that's so hot. The angst throughout the show between the couple is awesome. It's great as long as you don't have a problem with older women younger man coupling (which I don't)
2) Heart to Heart; I haven't finished it but I think around episode 3 or 4 there is literally one of my top 3 romance scenes like in general. I promise if you get through the first couple episodes you'll be hooked.
3) That's Okay; It's Love; Just one where they just you know, have a more intimate sexy scene but not as much as the first 2 above.
4) Birth of a Beauty; really really interesting and lots of angst.
and I Need Romance 3 would be on my list but... you already got that one hah.
Not only are these dramas filled with more romantic scenes and kissing but like you want the plots are mature and riveting.