ill make a list for you ლ(´ڡ`ლ) ill try to keep it with shounen ai but i hope youre OK with yaoi !!
http://www.mangago.me/read-manga/yowamushi_danshi_renai_hajimemasu/ (yaoi sorry chapter one is also a warning but they apologize in the next chapter)
http://www.mangago.me/read-manga/komatta_toki_ni_wa_hoshi_ni_kike/ (the ending is called unsatisfying and it is a long read, but i love it so much that the ending was very fitting imo)
http://www.mangago.me/read-manga/blood_bank/?av=1 (also yaoi and a long read, has bdsm fetish and i would highly recommend if it interests you)
http://www.mangago.me/read-manga/konna_nichijou/ (yaoi again and this is a "different strokes for different folks" manga haha)
http://www.mangago.me/read-manga/super_lovers/ (few sexual scenes and a longer read but i would recommend this, one of my top favs)
http://www.mangago.me/read-manga/danshi_koukouseiteki_kazoku_keikaku/ (yaoi again sorry, but this is again a very "you like it or dont" manga)
http://www.mangago.me/read-manga/ashita_wa_docchi_da/ (yaoi again, but i will always recommend this author as her stories never disappoint, one of my favs)
http://www.mangago.me/read-manga/devils_honey/ (link to chapter are in the comments if they havent reposted them yet, and yes its another yaoi but i highly recommend)
http://www.mangago.me/read-manga/ganbare_nakamura_kun/ (unsure if this fits either of your character requirements, but this story is narrated by the misunderstood character, highly recommend)
http://www.mangago.me/read-manga/shitteru_yo/ (this is a story that i think youll like as it fits your requirements, highly recc and this story is very cute, yaoi sorry)
http://www.mangago.me/read-manga/kijima_kun/ (another you like it or dont and a longer read, also a yaoi story. This is an iffy story but quite cute at the same time)
http://www.mangago.me/read-manga/tadatada_suki_to_iu_dake_de/ (highly recc this one, yaoi sorry.)
http://www.mangago.me/read-manga/iki_o_tomete_ugokanai_de/ (another yaoi but this story has a warning as there are rape flashbacks, the protagonist is not the one who did it though)
http://www.mangago.me/read-manga/nirameba_koi/ (hes not necessarily "misunderstood" but he is different than the rumors surrounding him is)
http://www.mangago.me/read-manga/rutta_to_kodama/ (same as nirameba koi, he owns his delinquent title, but isnt as cruel as the rumors say he is)
http://www.mangago.me/read-manga/sayonara_alpha/ (yaoi and closest to "gap moe"?)
http://www.mangago.me/read-manga/koi_wa_kamen_no_uchigawa_ni/ (very good first chapter, mc is called delinquent but contrary to rumors, he trying to be a hero)
http://www.mangago.me/read-manga/cafe_latte_rhapsody/ (doesnt really show the sex and is cute, but boring at points haha, would recommend the fluff though)
http://www.mangago.me/read-manga/ore_no_kirai_na_senpai/ (yaoi and his looks say playboy, but hes a lowkey playboy, but not really if that makes sense haha)
also sorry for straying of some of the things you wanted and chose similar stories, i just wanted the choose the closest to it i could get if that makes sense （/TДT)/
OMG THANK YOU SO MUCH
no problem !! (๑•ㅂ•)و✧
Bl manga with a character that has gap moe or a character that’s personality doesn’t match their appearance