Dramas & Movies Where Nothing Broke The FL and ML Apart

Boss and Me - based on Web novel written by same author as Love O2O

You have Weightlifting Fairy Kim Bok Joo on hold. It fits your description (including the ML's ex bit) and I'd recommend giving it another try. 

From your PTW list:

• Healer
  • Once they're together the leads never break up, but the ML does have to go underground / sort of into hiding at one point which means seeing the FL a bit less for a little while
  • Public displays of affection:
    • They kiss in front of the FL's dad and his employee once
    • The FL falls asleep on the ML's lap on the couch in the office break room once
    • Most of their skinship occurs when they're alone
• Bring It On, Ghost
  • There are a few scenes where the FL might seem clingy because she thinks the ML holds the key to finding out how she became a ghost if I remember correctly, but she's strong and normally quite independent
  • I don't recall them breaking up at any point
  • Public displays of affection:
    • While the ML has the ability to see ghosts, most people can't, so the FL is essentially invisible to others when they're in public together. That means that when they go on a date their public displays of affection are sort of private but the ML also does look a bit strange - for example when they kiss in public anyone walking by would think the ML was kissing empty air

Not in your lists yet: 

• Just Between Lovers
  • Once they're together the ML and FL don't break up, although there is a health-related scare at one point
  • Public displays of affection:
    • The ML and FL occasionally say or do things that show their feelings for each other while they're in public, but as far as I can recall no one particularly notices 
    • The FL does ask the ML to go to a hotel
• Live Up to Your Name 
  • They time travel to the past a bit, but it's mostly in modern times
  • The ML and FL are separated by a time-travel related issue for a bit, but they are reunited in the end
  • Public displays of affection:
    • They kiss and hold hands while walking along the beach
    • When the FL is hospitalized the ML sleeps on the FL's bed to keep her warm, but the FL kicks him off when her friend / the nurse walks in
• Queen In Hyun's Man (a few scenes in the past, but mostly modern times)
  • I don't recall them breaking up at any point, although I think the time travel separated them on a few occasions, but not permanently
  • Public displays of affection:
    • They hug in a public library
    • They kiss in the library's glass elevator when the elevator is empty but the library is not
• Marriage Contract
  • I don't recall them breaking up at any point, however it is implied that, at the end of the drama, the FL is not expected to live much longer
  • Public displays of affection:
    • The ML and FL share a quick kiss and hold hands at an amusement park

There's a chance there might be secondary couples in the dramas above, but if there are, they were so minor that I've completely forgotten them. 

Edit: just re-read the title of the thread. I've added notes about whether the leads break up or are separated.

Edit 2: I've added notes about public displays of affection based on what I can remember. None of the leads in the dramas above are as publicly affectionate as the leads in WFKBJ. 

 YashKnight:

I mainly gave it up coz the leads were too open (for me) in their love.

Ah, we might have very different taste then. Do you mind if I ask what kind of things in particular you don't like? For example do you prefer dramas where there isn't much skinship overall, or is it just that you don't like dramas where the leads have lots of public displays of affection? 

I'll tailor my recommendations accordingly.

 YashKnight:

the recs you gave are good and I will check them out, overall i don't like drama in which the leads be very open with their love like in strong woman do bong soon, when the ml tells the fl let's go somewhere or shows that he likes her that's fine but when they show too much skinship in public or act like two people crazy in love in public I find it too cringy for me to handle, also sorry if I offended your view or anything.

No worries, you definitely didn't offend me. I just want to add notes to my recommendations based on your preferences :)

Kill me Heal me

Healer

Live up to your name

1% of anything 

Just between Lovers

From 5 to 9

20th Century boy and girl

 fanitha:

Kill me Heal me

Healer

Live up to your name

1% of anything 

Just between Lovers

From 5 to 9

20th Century boy and girl

I will check out 20th-century boy and girl but aren't there two main couples in this drama also will check out live up to your name

 skaikru:

Black Knight

Not a fan of the main couple but it fits your criteria .

same i didn't like the main couple but i will see how the story goes

 AmberSteininger:

Something About 1 Percent sounds like what you're looking for

thank you, but I have already seen it, but thanks

 AH:

I've added notes about public displays of affection based on what I can remember. None of the leads in the dramas above are as publicly affectionate as the leads in WFKBJ. 

you really have to go through the extra work but thank you, some of them I was unsure of like queen in hyun's man but I am definitely gonna check them out thanks again.