I prefer the first The Quiz Show to The Quiz Show 2, but it's an unpopular opinion. I recommend still watching them in order (with a break between as the episodic stories are very similar (overall story slightly different)), that way in the second one you'll notice the little drops they make to the first one too. The first Quiz Show is very short anyway so it's worth a try.
I am not a big romance lover either and while most of the ones I can think of that are most similar have been been mentioned above, here are some more that may interest you (some similar, some a little different but all really good):
Bokura no Yuuki (Our Courage)- My absolute favourite drama, the bad quality is worth it. Mystery, Corruption, Friendship etc. - A meteor kills all the adults in a town and leaves only kids, and the town is quarantined, leaving only kids to fend for themselves.
Yakou Kanransha (Ferris Wheel at Night)- Murder mystery surrounding two neighboring families
JIN - I noticed a few historical dramas/movies on your list. I finished the series a few days ago and I'm still thinking about it. Historical, Medical, Friendship
Zeni Geba (Money Crazy) - Someone who will do anything for money.
Tobosha (Runaway) - A probation officer is suspected of killing his wife and attacking his son leaving him in a coma and goes on the run
Yasha (Monster) - Two twins who were born as the product of a cloning/gene altering experiment, and possess superhuman abilities, separated at birth, one evil, one good. About what happens when they meet & a mysterious virus that has appeared. Mystery, Action