I haven't seen Love Between the Lines, but I think I get what you're talking about - that cdrama way of narrowing the focus to the romance, with just enough attention paid to complications in the leads' lives to amp up the feels.
+1 for Amidst a Snowstorm of Love - it meets all six of your requirements, and it plays on the all romance, all the time channel. There's some plot related to the ML reconnecting with his past and just enough billiards to keep things moving - but it isn't a sports drama, it's a love story.
Road Home has a similar emotional intensity to AaSoL and Shine on Me, with the same level of priority given to the romance, and many, many scenes of the couple falling in love. It has five of your requirements. The one thing you'll have to decide about is if you're okay with flashbacks to school days. The couple are mature, though - it's a second chance romance. And the way they use the flashbacks is to evoke a sweet, sad mood about the fact that they broke up, and how much pain that put them both in, which of course makes them that much more romantic in the present.
+1 for Dali and the Cocky Prince - meets all your requirements. But it's different from Shine on Me, Road Home, and Amidst a Snowstorm of Love, in that it's jam-packed with comedy and murder mystery piled on top of the chemistry.
