Tokyo crazy paradise may fit pretty well. Chick isn't weak at all, and yakuza dude is rather possessive if my memory is correct.

Few favs
Comedy:
Kyou kara ore wa!!, Mx0, Angel Densetsu, Skip Beat, Ai Kora, The Devil King is Bored

Romance:
Hana to Akuma, No bra, Shinigami Trilogy, kindan no koi de ikou, Usagi Drop, Threads of Time, Girl Friends

Most under rated:
Kindan no koi de ikou, kyou kara ore wa!.
m0r l83r... maybe >_>

9 Banme no Musashi maybe? I wouldn't say the male lead is especially possessive though >.<

Alot of them are probably already on your list, but too lazy to check so yea:
Red River
Akagami no Shirayukihime
1/2 Prince Kinda I suppose?
Rasetsu no Hana
NG Life
Warau Kanoko-sama and Koi dano Ai dano
Venus Capriccio I only just started reading this one myself, but trust me, it's REAL good.

Well... I dunno how much they fit your descriptions but give them a shot?

MERI PURI!!! 😀

I didn't see it on your list, but I think you might totally love it!!!

You could try Obaka-chan Koigatariki. There are actually two male leads which are both kind of possessive (and sort of pushy) The fun thing about it is the female lead is strong physically but she does have her "weak" moments (the author kept it really natural though, like there's no "I'm crying because I can't stand seeing him with this girl" sort of thing) but she makes up for it really well that you have to forgive her.

Oh, also Charming Junkie! Female lead isn't actually cold, but she's definitely not an annoying pushover/clingy/dependent kind of girl.

...I feel like I haven't helped that much at all -___-

Edit: I forgot to mention Watashi ni xx Shinasai! Main male leads (again there are two) are really possessive. And the girl's strong as well, often misunderstood and assertive if I may add. Definitely fits your category 😃

Saruyama maybe ... 😕 😕 😕

[img]http://i397.photobucket.com/albums/pp54/starc62/CuteDuckDancing.gif[/img]

Im not sure- but maybe [/m]WATASHI NI XX SHINASAI! The lead is cold and strong.(Most of the time)
And- maybe [m]barajou no kiss?

Try Kare Kano, the male mc is definitely possessive with yanderish tendencies n d female mc is no pushover, she's actually diabolical n can handle probs without her boyfriend's help. I really loved the series, u would too. 😀

Hmm, first comes to mind is:
Tonari no Kaibutsu-kun
Namaikizakari.
Beauty Pop
Short Cake Cake
Kiss Zekkou Kiss
Joousama no Inu
Watashitachi ni wa kabe ga aru
Hana ni Arashi
Cynical Orange
Gokuraku Seishun Hockey Club - female lead personality same as the female lead in Beauty Pop
Koi Dano Ai Dano
Ouran High School Host Club
Akuma to Love Song - cold and brutally honest, only she falls in love a little quickly (for me anyway)
Hirunaka no Ryuusei - not so much as cold as being nonchalant about love and not showing her emotions much and being dense
and maybe Last Game? They're listed in the order that I think fits more in the characteristics you've requested. Hope that helped!

Other new mangas that also fit the category are:
Takane to Hana
Sabaku no Harem

PS. I'm tired of the usual weak shoujo protagonists too. 😀

"FEED YOUR OWN EGO, I'M BUSY."

i don't know if the girl is considered strong but she is definitely not weak. the manga is called soredemo sekai wa utsukushi

Bitter Trap (TAKAGI Shigeyoshi) a oneshot from Hyakujuu Kingdom
Hana no Kishi
Koroshi Ai
If you read webtoon maybe Cheese in the Trap, My Secret Brother or American Ghost Jack.
Tendou-ke Monogatari
Madame Petit
Or more recently Sekai de Ichiban Warui Majo I think it fits perfectly your description 😮
I hope I was able to help 😀 😀 😀 😀 😀 😀

Abide in the wind?

Show Princess - Definitely fits both requirements and the female lead can be cool-headed and one of the strongest fl i've encountered, because for her love is not the most important thing in her life.
The Prince's Cactus - fl outsmarts ml, and it is the ml that submits to fl first