I have come from the land of KDramas...

I've seen neither of those K-dramas yet, but TiMFL is often compared with NigeHaji --- you might try that out?

I personally don't watch a lot of J-romcoms/romances, but I can at least list some titles for you:

• Boku, Unmei no Hito desu- a popular 2017 drama
• Date - Koi to wa Donna Mono Kashira
• Proposal Daisakusen
• Koe Koi - a breezy and cute school romance drama 
• Love Shuffle
• Saikou no Rikon
• Manhatten Love Story
• Hana Yori Dango (S01, S02, + movie) - based on the same manga that Boys Over Flowers is adapted from
• Kimi wa Petto (2003 + 2017 remake)
• Rich Man, Poor Woman
• Hanazakari no Kimitachi e - To the Beautiful You is the Korean version
• If your willing to check out older stuff (like '90s), I'm told Japan made some good romances during that time. Titles I hear often: Long Vacation, Aoi Tori, Aishiteiru to Ittekure, Tokyo Love Story, and Virgin Road.

Some of these I've seen, some I haven't. I've seen all get their names tossed around quite a bit, though, when it comes to recs.

Some additional recs:

• Asuko March (school, romance)
  
• Zenkai Girl (romcom, my personal favorite)
  
• Love That Makes You Cry (drama, romance, haven't watched it myself but a lot of people seem to like it)
  
• Shitsuren Chocolatier (drama, not really a romance; dysfunctional relationships abound but I loved it; think of it as a makjang with a more realistic approach)
  
• Hotaru no Hikari (romcom)
  
• Gomen ne Seishun (comedy, school)
  
• Family's Form (family, drama, the romance is kinda light but if you like Because This is the First Time you might like this; it talked about what is family, what does being a family mean, if marriage means loss of individuality--that kinda thing, but not in a in-your-face way)
  
• Bara no nai Hanaya (drama, family, romance)
  
• Lunch Queen (drama, romance; reverse harem, sort of)
  

Here are my recommendations, some of them have already been mentioned:

• Hana yori dango – It’s a must see it’s the classical Cinderella story but one of the bests ever done (2 seasons and 1 movie). (Boys over flowers is the kversion of this drama)
• Buzzer Beat – Good romance drama about 2 people that meet and fall in love but first they have to find the perfect timing for them to be together
• Love Shuffle – It’s a story involving 4 couples and how they learn what love is
• Pride – A classic romance drama with a mature couple who grow and learn from each other and also heal each others wounds
• Tatta Hitotsu no koi – A very good romance and it’s a Cinderella story but inverse (rich girl, poor boy)
• Hotaru no Hikari – This has 2 seasons and a movie, and it’s a bout a couple that has to live together due to some circumstances and gradually fall in love
• We married as a job - As mentioned above this one is compared to Because this is my first life. I liked both of them but I'll have to say I liked better how they managed the "contract relationship" at the final episodes here. 
• Soratobu Kouhoushitsu - I like this one, because is also about 2 individuals who had their dreams broken about their ideal jobs but with the help of each other discover a new passion in life. 
• Kahogo no Kahoko - This one is pretty sweet and lighthearted, the OTP is very cute and it centers alot on family.
• Boku unmei no hito desu - This one is also pretty lighthearted, the male lead is very sweet and kind and it's totally focused on romance.
  
  

Thank you everyone for your recommendations! Now I have a whole list to choose from haha.