to be honest, the best dramas with those tropes you mention are from before 2014 because those were popular tropes back in the old days and they were done well, especially in Jdramas.
+1 for 1 Litre of Tears
I will also add another classic: Kamisama mou sukoshi dake (god please give me more time). YES it's from 1998, but there's a reason people are still watching it. Truly moving, the illness is AIDS which is unique in asian dramas. It's very easy to find online.
A modern rec I didn't see on your list: It's Okay, That's Love -- ML, FL, heck... almost every single character in it has mental health issues but it focuses on ML's. the "cry" part is not in the first half but the second half.