So, what I'm reading begs the question. If you (general you) want to basically swap stats and attributes to fit your theme (I want to have a high CHA fighter and use CHA bonuses in place of STR and DEX), then the question is, "Why have stats at all?" If we're going to make the bonuses totally replaceable and interchangeable, why have them at all? I'm not asking this as some sort of gotcha or sarcastic response, but an honest one.
Do you get rid of them completely and just go to something sorta skill based and bake them into the class?
Fighters: Gain a +3 bonus to hit and damage with attacks (to replicate STR or DEX)
Background: Choose strength based, agility, personality, intellect, or willpower based skills. Gain a +3 bonus to any saving throw or check when doing one of these skills.
That way you could have a fighter who gets the bonuses to attacks as "traditional" fighters, but can be personality rather than strength or dex if they choose.