I do apologize since it still is in progress, But send me a message with a couple of your reccomendations.
Im looking to make this a very user friendly set of builds for all Akali players. :D

Stacking bloodthirsters seems a tad on the odd side. Especially for Akali. AP stacking seems more appopriate.
This first build was more for the Akali that likes to run in fight and be able to actually take a few hits. The idea behind it was burst damage with a side of tank.

For the next builds I could use any and all suggestions,
-As I said in the introduction over the next few weeks I'd like to have 5 fantastic akali builds that anyone can adjust to. That way everyone feels comfortable playing in their own way. And they can do it successfully as well.

Yeah, Gunblade is 75ap, 50% Spell Vamp, and her Q scales a lot better with AP than her E does with AD.

Akali is BEST built AP because of her Ult+Q+Lich Bane combo.

Lich Bane + Rylai's is pretty core.

Deathcap + Gunblade + Void Staff/defensive item is usually Akali's Build.

(Mainly GA+Deathcap/Gunblade.)

ALSO Armor runes are very good on Akali.

Pointless AtS stacking is silly, if you want an auto attack bot, just play Madreds+Malady Teemo or something.

I believe a gunblade will give her more hp than building bloodthirsters
and she will do more damage by building more ap than just stacking bloodthirsters

ges not even needed >.> i was also experimating whit akali but her passive skil from attack demage is ownage becuase that also works as spel vamp her passive skil.

so my items as i recoment are

boots of mobilty
Bloodthirster
rabadons Deathcap
Bloodthirster
rulais scepter (for hp and slow)
or i buy another blood thirster or lichbane depents on what i want

this is my base hybrit style

and for runes i use abilty power at lvl 18 = ?
that is best for hybrit cus ability power is not realy what you need on akali its more attack cus that makes you get ur hp faster back and is also better for surviving

I would build some spell vamp on her. Like the Gunblade - works extremely well.

But I see you're still editing/updating :P