Since you are using a "Call A Shot" action between "Take Aim" and the actual shooting all your aiming will be lost.
You didn't read my post very well, I actually stated: "While the original order of actions was flawed, Call A Shot, Take Aim, Take Aim, Take Aim, Take Aim, Call A Shot, Fire Weapon is valid."
There is a Call A Shot before any Take Aim and one after them just before the Fire Weapon action. Both are allowed by RAW do to the following rules:
Call A Shot 1:
This action must be immediately followed by a Take Aim, Fire Weapon, Throw Weapon, or Melee Unarmed Attack.
Four Take Aims
then Call A Shot 2:
A character can aim and then call a shot at the time of the attack. Calling the shot is a Free Action.
Each Call A Shot meets the required criteria. #1 is followed by a Take Aim action, #2 occurs after the aim and at the time of the attack (specifically allowed in the text) and is immediately followed by the Fire Weapon action. All requirements have been met.