(Xbox 360) Character Customization Bug on 2nd Playthrough

After my first play through as the Jew character on the Xbox 360 version, I started a new game and found that no matter what class I picked, none of the makeup, eyewear, hair wigs, and helmet items show up on my character's head when equipped. I have started 4 new games, each time picking a different class just to test if it was a glitch specific to one of the classes.

What's very odd is that even though nothing from those inventory sections appear when equipped to my character, they are acknowledged by the game. One example is when attempting to recruit Token and putting on the gas mask. Even though it does not show the gas mask on my character in the inventory screen, when walking around in town, or in the cut scene with the guard, the game loads the proper cut scene allows me to progress and fight the guard. Another example is when in the school for the first time to rescue Craig and having freckles equipped when fighting the boss hall monitor to get the Day Walker achievement. 

I did not install the game to the hard drive and am playing directly from the disk so I cannot even try to remove the game itself from the hard drive and reinstall it to see if it clears up the issue. The only thing I have not tried yet is deleting every single save, dlc, any other related game data from the hard drive and then starting a new game. I would personally rather not have to lose any game saves since some are at specific points from my first play through that I wanted to keep.

Any assistance to clear this up would be appreciated since not being able to see what I am customizing on the head does take away from the game quite a bit.